# Overview: State-of-the-Art in the Energy Harvesting Based on Piezoelectric Devices for Last Decade

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Piezoelectric Materials and Energy-Harvesting Systems

#### 2.1. Common Background

#### 2.2. Material Performance

_{ij}for AlN are lower than those values of PZT (see Table 1), piezoelectric coupling is more advantageous due to its low dielectric constant and its high squared figure of merit related with the oscillation 33-mode (Q

_{33})

^{2}= d

_{33}g

_{33}(where d

_{33}, g

_{33}are the piezoelectric factors), creating a lead-free alternative to PZT FCs [92].

^{−3}for such structures [95] by measuring the peak short-circuit current and open circuit voltage for pulsed mechanical loading.

_{33}, d

_{31}and d

_{15}) of ZnO are relatively small in comparison with the corresponding factors of PZT (see Table 1). Computational investigations of dimensional effects in ZnO nanowires have shown that piezoelectric characteristics can be improved by reducing the diameter of the nanorods to about 1.5 nm [39]. At the same time, the modern methods of growing them allow for the obtainment of nanorods with a diameter in the range of 10–100 nm [96]. We also note the studies of nanoscale ferroelectrics in [97].

_{3}, LiNbO

_{3,}and PZT are actual semiconductors. For example, undoped PZT FC is a semiconductor with a band gap from 2.6 eV to 3.5 eV [17]. PZT FC also has p-type electrical conductivity due to the presence of low-valence impurities, which replace Pb-ions with higher valence. The material behavior changes due to the non-centrosymmetric crystalline structure, and this can be used to improve the work of appropriate devices, in particular photovoltaic characteristics or photochemical output.

#### 2.3. High-Temperature Application

_{C}< 600 °C. For example, ferroelectric materials based on PZT have T

_{C}< 400 °C, and a gradual decreasing in output power at temperatures up to 150 °C was reported for soft PZT energy harvesters [99].

_{ij}are not as high compared to ferroelectrics (see Table 1), GaN nanowires have already shown high piezoelectric factors [100], and piezoelectric sensors based on GaN [101] have been designed. Table 1 presents the piezoelectric factors of GaN nanowires and volumetric SCs. Due to their wideband gap, they are expected to operate in the limits of a broad temperature range while retaining low electrical conductivity. Moreover, being semiconductors, they have the possibility to be integrated with the electronics of energy harvesters. From the viewpoint of electronics, the sufficiently narrow band gap of silicon causes a deterioration in the functionality of the device at temperatures in the region of about 350–400 °C due to the significance of the intrinsic densities of electrons and holes in comparison with doping densities. The use of materials with wideband gap, such as GaN or SIC, is one of the possible decisions for energy harvesting in aggressive media [102].

_{3}is another candidate for high-temperature operations and was used in applications such as ultrasonic drills, samplers, and rock abrasion tools [104]. In shear conditions, LiNbO

_{3}SC demonstrates relatively high piezoelectric activity (see d

_{15}in Table 1) and ECFs necessary for effective energy transformation, as well as very high T

_{C}= 1142–1210 °C [105]. However, this material is still little used for energy harvesting [106].

#### 2.4. Polymer Piezoelectrics

_{3}) are inherently hard, having high stiffness and brittleness, fracturing at sufficiently low-tension loads [108]. Therefore, polymer materials with piezoelectric characteristics are of independent interest to energy harvesting due to their flexibility, low density (and correspondingly low weight), strength, biocompatibility, and small cost. Wearable and implantable devices are the examples of such applications [109,110], in which the polymer material bends or stretches due to limb motion or lung expansion during respiration [10]. The most common piezoelectric polymer is polyvinylidene fluoride (PVDF), known as a favorite polymer from the family of fluoropolymers, whose piezoelectric behavior is determined by oriented molecular dipoles, formed as the result of joint mechanical strain and electrical polarization of the ferroelectric β-phase of PVDF [108]. It has excellent thermal stability and mechanical strength. This polymer demonstrates a fracture strain of 2% or higher [10] but has relatively low piezoelectric factors d

_{ij}and ECFs k

_{ij}in comparison with the parameters of inorganic piezoelectrics (see Table 1). Moreover, it has a good processability and demonstrates chemical resistance to various aggressive media such as different acids, bases, organic solvents, oil, and fat. Examples of PVDF application in energy harvesting are associated with respiration by using microbelts [111], wind, and rainfall [112]. The manufacture methods of PVDF at the nano-scale have been developed by employing electro-spinning by using a needle [10] or disc [108] in order to form nano-fiber webs.

_{33}> 200 pC/N) and greater elasticity (s

_{11}≈ 1100 pPa

^{−1}) [114]. At the same time, they have low electromechanical coupling factors (k

_{33}< 0.1) and demonstrate a deterioration in output voltage at lower temperatures in comparison with PVDF [113].

#### 2.5. Optimization of Piezoelectric Materials and Energy Harvesters

_{3}); (ii) ceramic/crystal (PZT/α-Al

_{2}O

_{3}, PZT/ZnO, PZT/LiNbO

_{3}, and (Na, Li)NbO

_{3}/LiNbO

_{3}); and (iii) ceramics/metal (PZT/W, PZT/Mo, PZT/Pt, and PZT/Ni). The use of CMC technology can significantly improve the mechanical properties of ceramic materials. However, the problem of compromise of properties, that is, deterioration of electromechanical properties with an increase in the content of the passive phase, remains unresolved [85,134]. An interesting solution, proposed in recent years to improve both electrophysical and mechanical properties, is the development of piezoceramic materials with metallized pore surfaces [135,136,137].

- (i)
- The dynamic response of the harvesting construction;
- (ii)
- Electrical circuit providing generated voltage and charge;
- (iii)
- The related electromechanics of the system, which represents a key step in energy harvesting and presents a complex multiphysical problem.

_{ij}[150,153], which characterizes the effectiveness of transformating mechanical and electrical energy in a piezoelectric medium. In the case of dynamic applications, the obtained power for a given vibration medium is maximized [153,154,155]. In [155], a stress constraint was added to optimization for control of the peak stress in a piezoelectric and substrate composite system using linear elasticity so that the device could withstand the applied load or be repeatedly subjected to recoverable strain. In [149], by optimizing the dynamic system, the average effectiveness of energy transformation in stationary mode, similar to ECF, was used. Most dynamic optimization studies considered a single frequency medium, and the structural layout was optimized to tune its resonance modes to the excitement frequency. In [154], a cantilever-type energy harvester was optimized for broadband random oscillations. A comparison of solutions for objective functions and for a broadband medium shows that their topological constructions are fundamentally various. Thus, additional research is required in the field of dynamics and, in particular, for broadband and random environmental vibration conditions.

## 3. Piezoelectric Rotary Harvesters

#### 3.1. State-of-the-Art in Piezoelectric Harvesters

_{33}), axial (d

_{31}), and shear (d

_{15}) modes. A compressive force is applied to the piezoelectric material in the d

_{33}mode, while in the d

_{31}mode the piezoelectric patch is fixed on the console, and vibrations are created in the beam in order to create a bending strain in the piezoelectric patch. In the shear mode, the corresponding force is applied along the y-axis in the yz-plane, while the polarization direction remains along the x-axis [157].

^{3}can be achieved at a voltage of 3.8 V at a wind speed of 0.9 m/s. In [161], a windmill was constructed having a wind turbine with a horizontal axis and 12 magnets of variable polarity along the periphery. At the same time, a bimorphic PZT element with a size of 60 × 20 × 0.7 mm

^{3}had a magnet at its end. In this design, a peak electrical power of 450 µW can be achieved with a nominal wind speed of 4.2 miles per hour. In [162], a rotary harvester was proposed based on the vibration caused by the wind impact. A PVDF piezoelectric beam was used to maintain high deflection during impact. Analytical modeling was developed followed by the use of FE calculations. The maximum power of 2566.4 μW was achieved at a wind speed of 14 m/s.

_{15}) was present for collecting energy. The estimated power was approximately 16 mW with an external load of 3 MΩ.

_{15}) of a cantilever-type piezoelectric bimorphic energy harvester was used to satisfy the Timoshenko beam theory. The developed analytical model gave results close to finite-element modeling. Open circuit peak voltage and power obtained at optimal electric load resistance and operating resonant frequency were observed. Based on the Timoshenko beam theory, an energy harvester, operating in a shear mode (d

_{15}), is presented in [2]. The cantilever PZT sandwich beam was excited by the vibration of the base, causing shear deformation. It was found that the energy obtained in the d

_{15}mode was approximately 50% higher than the energy obtained in the d

_{33}mode. The data [177] showed that the value of d

_{15}is greater than the values of d

_{31}and d

_{33}. Therefore, a shear excitation mode of piezoelectric material should be used to capture power during rotational motion with a simple design of the structure.

#### 3.2. Some Solutions for Rotary Harvesters

#### 3.2.1. Rotary Harvester with Parallel Coaxial Plates

#### 3.2.2. Rotary Hub Energy Harvester

_{15}) can generate power of a higher value than the modes d

_{31}and d

_{33}. The maximum power of 113.6684 W was obtained in the harvester. The productivity of the harvester can be increased by increasing the radius of the hub and the number of levers in accordance with the power requirements.

#### 3.2.3. Shear-Mode Piezoelectric Energy Harvester with Scissor Mechanism

_{15}) mode [180]. The main parts of the suggested harvester included a windmill, a scotch-yoke mechanism, four piezoelectric pads with two scissor jacks, and two springs. A scissor mechanism with the scotch-yoke mechanism was used to transform the rotational motion of the wind turbine into linear oscillations of the piezoelectric pads. The force of the input spring was changed using a scissor mechanism. The principle of operation of the proposed generator is illustrated in Figure 3. The rotational motion of the input shaft was transformed into reciprocating motion by means of the scotch-yoke mechanism.

#### 3.2.4. Shear-Mode Piezoelectric Energy Harvester for Rotational Motion

_{15}) piezoelectric energy harvester was designed to collect energy from rotational motion. The assembly of the shear-mode (d

_{15}) rotary energy harvester is shown in Figure 4. The harvester consisted of a rotary hub, a stationary hub, and 2n PZT patches located on a fixed hub. The same number of magnets were located over the PZT patches, and n magnets of the same size were placed on a stationary hub so that the same poles of the magnets were in front of the face (see Figure 4). The relative angular motion between the stator and the rotor created a periodic magnetic repulsion force between the magnets and created a shear force on the PZT patches, which led to an electric charge on the surface of the PZT sections to collect energy.

## 4. Flexoelectric Effect

_{C}).

_{T}on opposite surfaces.

_{3}-coordinate consisted of the movement of w

_{c}(t) and the relative displacement of the beam w (x

_{1}, t). In the result of analytical modeling, the equation of an electrical circuit with a flexoelectric coupling was obtained.

## 5. Piezoelectric Generators

#### 5.1. Cantilever-Type PEG: Experiment

^{3}, obtained on the trapezoidal shape of the cantilever, exceeded the power of a rectangular shape of 0.6 μW/mm

^{3}.

#### 5.2. Some Solutions for Test Study of Cantilever-Type PEG with Proof Mass

_{i}= 1, 2, and 3 mm). The characteristic dependences of output electric power on load resistance for a proof mass of 20.6 g are present in Figure 12, defining a preferable result in a case of δ

_{3}= 3 mm.

_{l}= 10 kΩ was reached. The calculation showed that specific output electric power of this PEG model was equal to W

_{out}= 69.2 mW/cm

^{3,}which was three orders of magnitude higher in comparison with the cantilever PEG studied in [82].

#### 5.3. Cantilever-Type PEG: Modeling

#### 5.3.1. Cantilever-Type PEG with Symmetrical and Asymmetrical Location of Proof Mass

_{m}= 65 mm and 103.5 mm, Figure 15 presents dependencies of output voltage and output power on active load for these proof masses. The values of output voltage and output power, obtained in symmetric case, differed weakly on values of asymmetric case.

_{xy}are the first, second, fifth, and sixth oscillation modes. A transverse vibration mode in a horizontal plane O

_{xz}is the third oscillation mode. A torsion vibration mode with respect to the axis O

_{x}is the fourth mode.

_{0}is the vibrations amplitude and f is the forced oscillations frequency.

_{0}is the force amplitude.

#### 5.3.2. Cantilever-Type PEG, Based on Porous Piezoceramic, with Proof Mass

#### 5.3.3. Numerical Optimization of Cantilever-Type PEG with Incomplete Covering Substrate by Piezoelectric Elements

_{3}-axis. The electrical voltage v(t) was measured across resistor R. Finite-element analysis of an improved cantilever PEG model was carried out [9].

#### 5.3.4. Modeling Double-Console PEG

#### 5.3.5. Bistable and Tristable Energy Harvesting in Cardiology

^{2}.

#### 5.3.6. Wind Energy Harvesting from Artificial Grass

^{2}area. The wind striked with these cantilevers, deforming them, and energy of wind was transformed into electrical energy.

#### 5.4. Stack-Type PEG: Experiment

^{3}.

_{l}for the PEG sensitive element with an equivalent circuit that includes in parallel the electrical capacitance C

_{x}of the sensitive element and the active resistance R

_{x}was determined by the criterion: R

_{l}C

_{x}≥ τ

_{i}, where τ

_{i}is the duration of the compression force pulse.

_{c}= 17.2 MPa and various values of electric load resistance R

_{l}(see Figure 30). Peak values of output power in dependence on the quasistatic loading velocity of PEGs at various stack heights and PEG electric capacitances are present in Figure 31. Then, based on the measurement results, dependence of output voltage in dependence on electric load resistance and loading frequency (see Figure 32) was obtained. Moreover, output power for the PEG was also calculated, normalized by amplitude of mechanical load in dependence on electric load resistance and loading frequency (see Figure 33).

#### 5.5. Stack-Type PEG: Modeling

#### 5.6. Comparative Optimization of Cantilever-Type and Stack-Type PEGs

## 6. Concluding Remarks

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Harne, R.L.; Wang, K.W. A review of the recent research on vibration energy harvesting via bistable systems. Smart Mater. Struct.
**2013**, 22, 023001. [Google Scholar] [CrossRef] - Malakooti, M.H.; Sodano, H.A. Piezoelectric energy harvesting through shear mode operation. Smart Mater. Struct.
**2015**, 24, 055005. [Google Scholar] [CrossRef] - Paulo, J.; Gaspar, P. Review and future trend of energy harvesting methods for portable medical devices. In Proceedings of the World Congress on Engineering 2010 (WCE 2010), London, UK, 30 June–2 July 2010; 2010; Volume II. Available online: http://www.iaeng.org/publication/WCE2010/WCE2010_pp909-914.pdf (accessed on 2 December 2021).
- Pellegrini, S.P.; Tolou, N.; Schenk, M.; Herder, J.L. Bistable vibration energy harvesters: A review. J. Intell. Mater. Syst. Struct.
**2013**, 24, 1303–1312. [Google Scholar] [CrossRef] - Shaikh, F.K.; Zeadally, S. Energy harvesting in wireless sensor networks: A comprehensive review. Renew. Sustain. Rev.
**2016**, 55, 1041–1054. [Google Scholar] [CrossRef] - Wang, Z.L.; Zhu, G.; Yang, Y.; Wang, S.; Pan, C. Progress in nanogenerators for portable electronics. Mater. Today
**2012**, 15, 532–543. [Google Scholar] [CrossRef] - Guo, X.; Liu, L.; Zhang, Z.; Gao, S.; He, T.; Shi, Q.; Lee, C. Technology evolution from micro-scale energy harvesters to nanogenerators. J. Micromechanics Microengineering
**2021**, 31, 093002. [Google Scholar] [CrossRef] - Nechibvute, A.; Chawanda, A.; Luhanga, P. Piezoelectric energy harvesting devices: An alternative energy. Smart Mater. Res.
**2012**, 2012, 853481. [Google Scholar] [CrossRef][Green Version] - Soloviev, A.N.; Parinov, I.A.; Cherpakov, A.V.; Chebanenko, V.A.; Rozhkov, E.V. Analysing the Output Characteristics of a Double-console PEG Based on Numerical Simulation. Mater. Phys. Mech.
**2018**, 37, 168–175. [Google Scholar] [CrossRef] - Qi, Y.; McAlpine, M.C. Nanotechnology-enabled flexible and biocompatible energy harvesting. Energy Environ. Sci.
**2010**, 3, 1275–1285. [Google Scholar] [CrossRef] - Radousky, H.B.; Liang, H. Energy harvesting: An integrated view of materials, devices and applications. Nanotechnology
**2012**, 23, 502001. [Google Scholar] [CrossRef] - Wang, H.; Jasim, A.; Chen, X. Energy harvesting technologies in roadway and bridge for different applications–A comprehensive review. Appl. Energy
**2018**, 212, 1083–1094. [Google Scholar] [CrossRef] - Wang, X. Piezoelectric nanogenerators−Harvesting ambient mechanical energy at the nanometer scale. Nano Energy
**2012**, 1, 13–24. [Google Scholar] [CrossRef] - Wang, Z.L. From nanogenerators to piezotronics—A decade long study of ZnO nanostrucutres. MRS Bull.
**2012**, 37, 814–827. [Google Scholar] [CrossRef][Green Version] - Wang, Z.L. Progress in piezotronics and piezo-phototronics. Adv. Mater.
**2012**, 24, 4632–4646. [Google Scholar] [CrossRef] [PubMed] - Wang, Z.L.; Wu, W. Nanotechnology enabled energy harvesting for self-powered micro/nanosystems. Angew. Chem.
**2012**, 51, 11700–11721. [Google Scholar] [CrossRef] [PubMed] - Bowen, C.R.; Topolov, V.Y.; Kim, H.A. (Eds.) Modern Piezoelectric Energy-Harvesting Materials. Springer Series in Materials Science; Springer: Cham, Switzerland, 2016; Volume 238. [Google Scholar] [CrossRef]
- Li, L.; Xu, J.; Liu, J.; Gao, F. Recent progress on piezoelectric energy harvesting: Structures and materials. Adv. Compos. Hybrid Mater.
**2018**, 1, 478–505. [Google Scholar] [CrossRef] - Maurya, D.; Yan, Y.; Priy, S. Piezoelectric Materials for Energy Harvesting. In Advanced Materials for Clean Energy; Xu, Q., Jo, K., Kobayashi, T., Eds.; CRC Press: Boca Raton, FA, USA, 2015; pp. 143–178. [Google Scholar] [CrossRef]
- Husain, A.A.F.; Hasan, W.Z.W.; Shafie, S.; Hamidon, M.N.; Pandey, S.S. A review of transparent solar photovoltaic technologies. Renew. Sustain. Energy Rev.
**2018**, 94, 779–791. [Google Scholar] [CrossRef] - Ng, C.H.; Lim, H.N.; Hayase, S.; Zainal, Z.; Huang, N.M. Photovoltaic performances of mono-and mixed-halide structures for perovskite solar cell: A review. Renew. Sustain. Energy Rev.
**2018**, 90, 248–274. [Google Scholar] [CrossRef] - Tiwari, G.N.; Mishra, R.K.; Solanki, S.C. Photovoltaic modules and their applications: A review on thermal modelling. Appl. Energy
**2011**, 88, 2287–2304. [Google Scholar] [CrossRef] - Wang, Z.L.; Yang, R.; Zhou, J.; Qin, Y.; Xu, C.; Hu, Y.; Xu, S. Lateral nanowire/nanobelt based nanogenerators, piezotronics and piezo-phototronics. Mater. Sci. Eng. R. Rep.
**2010**, 70, 320–329. [Google Scholar] [CrossRef] - Hunter, S.R.; Lavrik, N.V.; Mostafa, S.; Rajic, S.; Datskos, P.G. Review of pyroelectric thermal energy harvesting and new MEMs-based resonant energy conversion techniques. SPIE Def. Secur. Sens.
**2012**, 8377, 83770D. [Google Scholar] [CrossRef] - Junior, O.H.A.; Maran, A.L.O.; Henao, N.C. A review of the development and applications of thermoelectric microgenerators for energy harvesting. Renew. Sustain. Energy Rev.
**2018**, 91, 376–393. [Google Scholar] [CrossRef] - Khan, F.U.; Qadir, M.U. State-of-the-art in vibration-based electrostatic energy harvesting. J. Micromechanics Microengineering
**2016**, 26, 103001. [Google Scholar] [CrossRef] - Narita, F.; Fox, M. A review on piezoelectric, magnetostrictive, and magnetoelectric materials and device technologies for energy harvesting applications. Adv. Eng. Mater.
**2018**, 20, 1700743. [Google Scholar] [CrossRef][Green Version] - Saadon, S.; Sidek, O. A review of vibration-based MEMS piezoelectric energy harvesters. Energy Convers. Manag.
**2011**, 52, 500–504. [Google Scholar] [CrossRef] - Ahmed, R.; Mir, F.; Banerjee, S. A review on energy harvesting approaches for renewable energies from ambient vibrations and acoustic waves using piezoelectricity. Smart Mater. Struct.
**2017**, 26, 085031. Available online: https://iopscience.iop.org/article/10.1088/1361-665X/aa7bfb (accessed on 2 April 2022). [CrossRef] - Kim, H.S.; Kim, J.H.; Kim, J. A review of piezoelectric energy harvesting based on vibration. Int. J. Precis. Eng. Manuf.
**2011**, 12, 1129–1141. [Google Scholar] [CrossRef] - Parinov., I.; Chang, S.H.; Topolov, V. (Eds.) Advanced Materials. Manufacturing, Physics, Mechanics and Applications. Springer Proceedings in Physics; Springer: Cham, Switzerland, 2016; Volume 175, p. 707. [Google Scholar] [CrossRef]
- Advanced Materials. PHENMA 2017. Springer Proceedings in Physics; Parinov, I.; Chang, S.H.; Gupta, V. (Eds.) Springer: Cham, Switzerland, 2018; Volume 207, p. 640. [Google Scholar] [CrossRef]
- Parinov, I.; Chang, S.H.; Gupta, V. (Eds.) Advanced Materials. PHENMA 2018. Springer Proceedings in Physics; Springer: Cham, Switzerland, 2019; Volume 224, p. 666. [Google Scholar] [CrossRef]
- Parinov, I.; Chang, S.H.; Gupta, V. (Eds.) Advanced Materials. PHENMA 2019. Springer Proceedings in Materials; Springer: Cham, Switzerland, 2020; Volume 6, p. 621. [Google Scholar] [CrossRef]
- Chang, S.-H.; Parinov, I.A.; Topolov, V.Y. (Eds.) Advanced Materials. Physics, Mechanics and Applications. Springer Proceedings in Physics; Springer: Cham, Switzerland, 2014; Volume 152, p. 380. [Google Scholar] [CrossRef]
- Parinov, I.A.; Chang, S.H.; Theerakulpisut, S. (Eds.) Advanced Materials. Studies and Applications; Nova Science Publishers: Hauppauge, NY, USA, 2015; p. 527. Available online: https://novapublishers.com/shop/advanced-materials-studies-and-applications (accessed on 2 April 2022).
- Parinov, I.A.; Chang, S.H.; Jani, M. (Eds.) Advanced Materials. Techniques, Physics, Mechanics and Applications. Springer Proceedings in Physics; Springer: Cham, Switzerland, 2017; Volume 193, p. 637. [Google Scholar] [CrossRef]
- Parinov, I.A. (Ed.) Advanced Nano- and Piezoelectric Materials and Their Applications; Nova Science Publishers: Hauppauge, NY, USA, 2014; p. 250. Available online: https://novapublishers.com/shop/advanced-nano-and-piezoelectric-materials-and-their-applications/ (accessed on 2 April 2022).
- Akopyan, V.A.; Soloviev, A.N.; Parinov, I.A.; Shevtsov, S.N. Definition of Constants for Piezoceramic Materials; Nova Science Publishers: Hauppauge, NY, USA, 2010; Available online: http://www.novapublishers.org/catalog/product_info.php?products_id=11404 (accessed on 2 April 2022).
- Parinov, I.A. (Ed.) Ferroelectrics and Superconductors: Properties and Applications; Nova Science Publishers: Hauppauge, NY, USA, 2012; 287p, Available online: http://www.novapublishers.org/catalog/product_info.php?products_id=24233 (accessed on 2 April 2022).
- Khanbareh, H.; Topolov, V.Y.; Bowen, C.R. Piezo-Particulate Composites. Manufacturing, Properties, Applications, Springer Series in Materials Science; Springer: Cham, Switzerland, 2019; Volume 283. [Google Scholar] [CrossRef]
- Parinov, I.A. (Ed.) Nano- and Piezoelectric Technologies, Materials and Devices; Nova Science Publishers: Hauppauge, NY, USA, 2013; p. 261. Available online: https://novapublishers.com/shop/nano-and-piezoelectric-technologies-materials-and-devices/ (accessed on 2 April 2022).
- Parinov, I.A. Microstructure and Properties of High-Temperature Superconductors, 2nd ed.; Springer: Heidelberg, Germany, 2013; 779p. [Google Scholar] [CrossRef][Green Version]
- Parinov, I.; Chang, S.H. (Eds.) Physics and Mechanics of New Materials and Their Applications; Nova Science Publishers: Hauppauge, NY, USA, 2013; 444p, Available online: https://novapublishers.com/shop/physics-and-mechanics-of-new-materials-and-their-applications/ (accessed on 2 April 2022).
- Parinov, I.A.; Chang, S.H.; Kim, Y.H.; Noda, N.A. (Eds.) Physics and Mechanics of New Materials and Their Applications. PHENMA 2020. Springer Proceedings in Materials. Springer: Cham, Switzerland, 2021; Volume 10, 601p. [Google Scholar] [CrossRef]
- Parinov, I.A. (Ed.) Piezoceramic Materials and Devices; Nova Science Publishers: Hauppauge, NY, USA, 2010; p. 335. Available online: http://www.novapublishers.org/catalog/product_info.php?products_id=11605 (accessed on 2 April 2022).
- Parinov, I.A. (Ed.) Piezoelectric Materials and Devices; Nova Science Publishers: Hauppauge, NY, USA, 2012; p. 328. Available online: www.novapublishers.org/catalog/product_info.php?products_id=20009 (accessed on 2 April 2022).
- Parinov, I.A. (Ed.) Piezoelectrics and Nanomaterials: Fundamentals, Developments and Applications; Nova Science Publishers: Hauppauge, NY, USA, 2015; p. 283. Available online: https://novapublishers.com/shop/piezoelectrics-and-nanomaterials-fundamentals-developments-and-applications/ (accessed on 2 April 2022).
- Parinov, I.A. (Ed.) Piezoelectrics and Related Materials: Investigations and Applications; Nova Science Publishers: Hauppauge, NY, USA, 2012; p. 306. Available online: http://www.novapublishers.org/catalog/product_info.php?products_id=30669 (accessed on 2 April 2022).
- Rybyanets, A.N. Microstructural Features, Electrophysical Properties and Wave Processes in Spatially Inhomogeneous Ferroactive and Dissipative Media. Ph.D. Thesis, Southern Federal University, Rostov-on-Don, Russia, 2018. (In Russian). [Google Scholar]
- Topolov, V.Y. Heterogeneous Ferroelectric Solid Solutions. Phases and Domain States. Springer Series in Materials Science, 2nd ed.; Springer: Cham, Switzerland, 2018; Volume 151. [Google Scholar] [CrossRef]
- Topolov, V.Y.; Bisegna, P.; Bowen, C.R. Piezoactive Composites. Orientation Effects and Anisotropy Factors. Springer Series in Materials Science; Springer: Cham, Switzerland, 2014; Volume 185. [Google Scholar] [CrossRef]
- Topolov, V.Y.; Bowen, C.R.; Bisegna, P. Piezo-Active Composites. Microgeometry–Sensitivity Relations. Springer: Cham, Switzerland, 2018; Volume 271. [Google Scholar] [CrossRef]
- Uchino, K. Piezoelectric energy harvesting systems—Essentials to successful developments. Energy Technol.
**2018**, 6, 829–848. [Google Scholar] [CrossRef] - Erturk, A. Piezoelectric energy harvesting for civil infrastructure system applications: Moving loads and surface strain fluctuations. J. Intell. Mater. Syst. Struct.
**2011**, 22, 1959–1973. [Google Scholar] [CrossRef] - Le, M.Q.; Capsal, J.-F.; Lallart, M.; Hebrard, Y.; Van Der Ham, A.; Reffe, N.; Geynet, L.; Cottinet, P.-J. Review on energy harvesting for structural health monitoring in aeronautical applications Prog. Aerosp. Sci.
**2015**, 79, 147–157. [Google Scholar] [CrossRef] - Shevtsov, S.N.; Soloviev, A.N.; Parinov, I.A.; Cherpakov, A.V.; Chebanenko, V.A. Piezoelectric Actuators and Generators for Energy Harvesting. Innovation and Discovery in Russian Science and Engineering; Springer: Cham, Switzerland, 2018. [Google Scholar] [CrossRef]
- Safaei, M.; Sodano, H.A.; Anton, S.R. A review of energy harvesting using piezoelectric materials: State-of-the-art a decade later (2008–2018). Smart Mater. Struct.
**2019**, 28, 113001. [Google Scholar] [CrossRef] - Zhang, Y.; Wang, T.; Luo, A.; Hu, Y.; Li, X.; Wang, F. Micro electrostatic energy harvester with both broad bandwidth and high normalized power density. Appl. Energy
**2018**, 212, 362–371. [Google Scholar] [CrossRef] - Zhang, Y.; Wang, T.; Zhang, A.; Peng, Z.; Luo, D.; Chen, R.; Wang, F. Electrostatic energy harvesting device with dual resonant structure for wideband random vibration sources at low frequency. Rev. Sci. Instrum.
**2016**, 87, 125001. [Google Scholar] [CrossRef] [PubMed] - Banerji, S.; Bagchi, A.; Khazaeli, S. Energy harvesting methods for structural health monitoring using wireless sensors: A review. Resilient Infrastruct. Lond.
**2016**, 2016, 1–10. [Google Scholar] - Tan, Y.; Dong, Y.; Wang, X. Review of MEMS electromagnetic vibration energy harvester. J. Microelectromechanical Syst.
**2017**, 26, 1–16. [Google Scholar] [CrossRef] - Saxena, P.; Shukla, P. A comprehensive review on fundamental properties and applications of poly(vinylidene fluoride) (PVDF). Adv. Compos. Hybrid Mater.
**2021**, 4, 8–26. [Google Scholar] [CrossRef] - Wang, Z.L. Triboelectric nanogenerators as new energy technology and self-powered sensors—Principles, problems and perspectives. Faraday Discuss.
**2015**, 176, 447–458. [Google Scholar] [CrossRef] - Xu, L.; Jiang, T.; Lin, P.; Shao, J.J.; He, C.; Zhong, W.; Chen, X.Y.; Wang, Z.L. Coupled triboelectric nanogenerator networks for efficient water wave energy harvesting. ACS Nano
**2018**, 12, 1849–1858. [Google Scholar] [CrossRef] - Anton, S.R. Multifunctional Piezoelectric Energy Harvesting Concepts. Ph.D. Thesis, Virginia Polytechnic Institute and State University, Blackburn, VA, USA, 2011. [Google Scholar]
- Chebanenko, V.A.; Akopyan, V.A.; Parinov, I.A. Piezoelectric Generators and Energy Harvesters: Modern State of the Art. In Piezoelectrics and Nanomaterials: Fundamentals, Developments and Applications; Parinov, I.A., Ed.; Nova Science Publishers: Hauppauge, NY, USA, 2015; pp. 243–277. Available online: https://novapublishers.com/shop/piezoelectrics-and-nanomaterials-fundamentals-developments-and-applications/ (accessed on 2 April 2022).
- Erturk, A.; Inman, D.J. Piezoelectric Energy Harvesting; John Wiley & Sons: Hoboken, NJ, USA, 2011. [Google Scholar]
- Guyomar, D.; Lallart, M. Recent Progress in Piezoelectric Conversion and Energy Harvesting Using Nonlinear Electronic Interfaces and Issues in Small Scale Implementation. Micromachines
**2011**, 2, 274–294. [Google Scholar] [CrossRef][Green Version] - Grudén, M.; Hinnemo, M.; Dancila, D.; Zherdev, F.; Edvinsson, N.; Brunberg, K.; Andersson, L.; Byström, R.; Rydberg, A. Field operational testing for safety improvement of freight trains using wireless monitoring by sensor network. IET Wirel. Sens. Syst.
**2014**, 4, 54–60. [Google Scholar] [CrossRef] - Tianchen, Y.; Jian, Y.; Ruigang, S.; Xiaowei, L. Vibration energy harvesting system for railroad safety based on running vehicles. Smart Mater. Struct.
**2014**, 23, 125046. [Google Scholar] [CrossRef] - Zhu, M.; Edkins, S. Analytical modelling results of piezoelectric energy harvesting devices for self-power sensors/sensor networks in structural health monitoring. Procedia Eng.
**2011**, 25, 195–198. [Google Scholar] [CrossRef][Green Version] - Abdelkefi, A.; Ghommem, M. Piezoelectric energy harvesting from morphing wing motions for micro air vehicles. Theor. Appl. Mech. Lett.
**2013**, 3, 052004. [Google Scholar] [CrossRef][Green Version] - Fu, X.; Hosta-Rigau, L.; Chandrawati, R.; Cui, J. Multi-Stimuli-Responsive Polymer Particles, Films, and Hydrogels for Drug Delivery. Chem
**2018**, 4, 2084–2107. [Google Scholar] [CrossRef][Green Version] - Hatai, J.; Hirschhäuser, C.; Niemeyer, J.; Schmuck, C. Multi-Stimuli-Responsive Supramolecular Polymers Based on Noncovalent and Dynamic Covalent Bonds. ACS Appl. Mater. Interfaces
**2020**, 12, 2107–2115. [Google Scholar] [CrossRef] - Schattling, P.; Jochum, F.D.; Theato, P. Multi-stimuli responsive polymers—the all-in-one talents. Polym. Chem.
**2014**, 5, 25–36. [Google Scholar] [CrossRef] - Shevtsov, S.; Akopyan, V.; Rozhkov, E.; Chebanenko, V.; Yang, C.-C.; Lee, C.-Y.J.; Kuo, C.-X. Optimization of the Electric Power Harvesting System Based on the Piezoelectric Stack Transducer. In Advanced Materials. Springer Proceedings in Physics; Parinov., I., Chang, S.H., Topolov, V., Eds.; Springer: Cham, Switzerland, 2016; Volume 175, pp. 639–650. [Google Scholar] [CrossRef]
- Soloviev, A.N.; Chebanenko, V.A.; Parinov, I.A. Mathematical Modelling of Piezoelectric Generators on the Base of the Kantorovich Method. In Analysis and Modelling of Advanced Structures and Smart Systems. Advanced Structured Materials; Altenbach, H., Carrera, E., Kulikov., G., Eds.; Springer: Singapore, 2018; Volume 81, pp. 227–258. [Google Scholar] [CrossRef]
- Wang, J.; Shi, Z.; Han, Z. Analytical solution of piezoelectric. composite stack transducers. J. Intell. Mater. Syst. Struct.
**2013**, 24, 1626–1636. [Google Scholar] [CrossRef] - Zhao, S.; Erturk, A. Deterministic and band-limited stochastic energy harvesting from uniaxial excitation of a multilayer piezoelectric stack. Sens. Actuators A: Phys.
**2014**, 214, 58–65. [Google Scholar] [CrossRef] - Akopyan, V.A.; Parinov, I.A.; Zakharov, Y.N.; Chebanenko, V.A.; Rozhkov, E.V. Advanced Investigations of Energy Efficiency of Piezoelectric Generators. In Advanced Materials. Studies and Applications; Parinov, I.A., Chang, S.H., Theerakulpisut, S., Eds.; Nova Science Publishers: Hauppauge, NY, USA, 2015; pp. 417–436. Available online: https://novapublishers.com/shop/advanced-materials-studies-and-applications/ (accessed on 2 April 2022).
- Akopyan, V.A.; Zakharov, Y.N.; Parinov, I.A.; Rozhkov, E.V.; Shevtsov, S.N.; Chebanenko, V.A. Optimization of output characteristics of the bimorph power harvesters. In Nano- and Piezoelectric Technologies, Materials and Devices; Parinov, I.A., Ed.; Nova Science Publishers: Hauppauge, NY, USA, 2013; pp. 111–131. Available online: https://novapublishers.com/shop/nano-and-piezoelectric-technologies-materials-and-devices/ (accessed on 2 April 2022).
- Soloviev, A.N.; Parinov, I.A.; Cherpakov, A.V.; Chebanenko, V.A.; Rozhkov, E.V.; Duong, L.V. Analysis of the performance of the cantilever type piezoelectric generator based on finite element modeling. In Advances in Structural Integrity; Prakash, R., Jayaram, V., Saxena, A., Eds.; Springer: Singapore, 2018; pp. 291–301. [Google Scholar] [CrossRef]
- Gusev, A.A.; Avvakumov, E.G.; Isupov, V.P.; Reznichenko, L.A.; Verbenko, I.A.; Miller, A.I.; Cherpakov, A.V. Mechanochemical Synthesis of Piezoelectrics on the Base of Lead Zirconate Titanate. In Piezoelectric Materials and Devices; Parinov, I.A., Ed.; Nova Science Publishers: Hauppauge, NY, USA, 2012; pp. 189–234. Available online: www.novapublishers.org/catalog/product_info.php?products_id=20009 (accessed on 2 April 2022).
- Khasbulatov, S.; Cherpakov, A.; Parinov, I.; Andryushin, K.; Shlkina, L.; Aleshin, V.; Andryushina, I.; Mardaliev, B.; Gordienko, D.; Verbenko, I.; et al. Destruction phenomena in ferroactive materials. J. Adv. Dielectr.
**2020**, 10, 2050012. [Google Scholar] [CrossRef] - Bowen, C.R.; Kim, H.A.; Weaver, P.M.; Dunn, S. Piezoelectric and ferroelectric materials and structures for energy harvesting applications. Energy Environ. Sci.
**2014**, 7, 25–44. [Google Scholar] [CrossRef][Green Version] - Eliseev, E.A.; Morozovska, A.N.; Svechnikov, G.S.; Gopalan, V.; Shur, V.Y. Static conductivity of charged domain walls in uniaxial ferroelectric semiconductors. Phys. Rev. B
**2011**, 83, 235313. [Google Scholar] [CrossRef][Green Version] - Ghara, S.; Geirhos, K.; Kuerten, L.; Lunkenheimer, P.; Tsurkan, V.; Fiebig, M.; Kézsmárki, I. Giant conductivity of mobile non-oxide domain walls, Nat. Commun.
**2021**, 12, 3975. [Google Scholar] [CrossRef] - Werner, C.S.; Herr, S.J.; Buse, K.; Sturman, B.; Soergel, E.; Razzaghi, C.; Breunig, I. Large and accessible conductivity of charged domain walls in lithium niobate. Sci. Rep.
**2017**, 7, 9862. [Google Scholar] [CrossRef] [PubMed] - Betts, D.N.; Kim, H.A.; Bowen, C.R.; Inman, D.J. Optimal configurations of bistable piezo-composites for energy harvesting. Appl. Phys. Lett.
**2012**, 100, 114104. [Google Scholar] [CrossRef][Green Version] - Kim, S.; Priya, S.; Kanno, I. Piezoelectric MEMS for energy harvesting. MRS Bull.
**2012**, 37, 1039–1050. [Google Scholar] [CrossRef][Green Version] - Andosca, R.; McDonald, T.G.; Genova, V.; Rosenberg, S.; Keating, J.; Benedixen, C.; Wu, J. Experimental and theoretical studies on MEMS piezoelectric vibrational energy harvesters with mass loading. Sens. Actuators A Phys.
**2012**, 178, 76–87. [Google Scholar] [CrossRef] - Briscoe, J.; Bilotti, E.; Dunn, S. Measured efficiency of a ZnO nanostructured diode piezoelectric energy harvesting device. Appl. Phys. Lett.
**2012**, 101, 093902. [Google Scholar] [CrossRef] - Zhilin, D.A.; Karapetyan, G.Y.; Kutepov, M.E.; Minasyan, T.A.; Yatsenko, V.I.; Kaidashev, E.M. Growth and Study of Zinc Oxide Nanorods Arrays on Piezoelectric Substrates. In Advanced Materials. PHENMA 2017. Springer Proceedings in Physics; Parinov, I., Chang, S.H., Gupta, V., Eds.; Springer: Cham, Switzerland, 2018; Volume 207, pp. 25–31. [Google Scholar] [CrossRef]
- Hu, Y.; Lin, L.; Zhang, Y.; Wang, Z. Replacing a battery by a nanogenerator with 20 V output. Adv. Mater.
**2012**, 24, 110–114. [Google Scholar] [CrossRef] - Espinosa, H.D.; Bernal, R.A.; Minary-Jolandan, M. A review of mechanical and electromechanical properties of piezoelectric nanowires. Adv. Mater.
**2012**, 24, 4656–4675. [Google Scholar] [CrossRef] - Varghese, J.; Whatmore, R.W.; Holmes, J.D. Ferroelectric nanoparticles, wires and tubes: Synthesis, characterisation and applications. J. Mater. Chem. C
**2013**, 1, 2618–2638. [Google Scholar] [CrossRef][Green Version] - Briscoe, J.; Jalali, N.; Woolliams, P.; Stewart, M.; Weaver, P.M.; Cain, M.; Dunn, S. Measurement techniques for piezoelectric nanogenerators. Energy Environ. Sci.
**2013**, 6, 3035–3045. [Google Scholar] [CrossRef] - Kim, S.; Park, J.; Ahn, H.; Liu, D.; Kim, D. Temperature effects on output power of piezoelectric vibration energy harvesters. Microelectron. J.
**2011**, 42, 988–991. [Google Scholar] [CrossRef] - Minary-Jolandan, M.; Bernal, R.A.; Kuljanishvili, I.; Parpoil, V.; Espinosa, H.D. Individual GaN nanowires exhibit strong piezoelectricity in 3D. Nano Lett.
**2012**, 12, 970–976. [Google Scholar] [CrossRef] - Le Boulbar, E.D.; Edwards, M.J.; Vittoz, S.; Vanko, G.; Brinkfeldt, K.; Rufer, L.; Johander, P.; Lalinský, T.; Bowen, C.R.; Allsopp, D.W.E. Effect of bias conditions on pressure sensors based on AlGaN/GaN high electron mobility transistor. Sens. Actuators A Phys.
**2013**, 194, 247–251. [Google Scholar] [CrossRef] - Kudimi, J.M.R.; Mohd-Yasin, F.; Dimitrijev, S. SiC-based piezoelectric energy harvester for extreme environment. Procedia Eng.
**2012**, 47, 1165–1172. [Google Scholar] [CrossRef][Green Version] - Hou, R.; Hutson, D.; Kirk, K.J.; Fu, Y.Q. AlN thin film transducers for high temperature non-destructive testing. J. Appl. Phys.
**2012**, 111, 074510. [Google Scholar] [CrossRef] - Bao, X.; Bar-Cohen, Y.; Scott, J.; Sherrit, S.; Widholm, S.; Badescu, M.; Shrout, T.; Jones, B. Ultrasonic/sonic drill for high temperature application. Proc. SPIE Sens. Smart Struct. Technol. Civ. Mech. Aerosp. Syst.
**2010**, 7647, 764739. [Google Scholar] [CrossRef] - Baba, A.; Searfass, C.T.; Tittmann, B.R. High temperature ultrasonic transducer up to 1000 °C using lithium niobate single crystal. Appl. Phys. Lett.
**2010**, 97, 232901. [Google Scholar] [CrossRef] - Lewis, R.W.C.; Allsopp, D.W.F.; Shields, P.; Šatka, A.; Yu, S.; Topolov, V.Y.; Bowen, C.R. Nano-imprinting of highly ordered mano-pillars of lithium niobate (LiNbO
_{3}). Ferroelectrics**2012**, 429, 62–68. [Google Scholar] [CrossRef][Green Version] - Zhang, S.; Yu, F. Piezoelectric materials for high temperature sensors. J. Am. Ceram. Soc.
**2011**, 94, 3153–3170. [Google Scholar] [CrossRef] - Fang, J.; Niu, H.; Wang, H.; Wang, X.; Lin, T. Enhanced mechanical energy harvesting using needleless electrospun poly(vinylidene fluoride) nanofibre webs. Energy Environ. Sci.
**2013**, 6, 2196–2202. [Google Scholar] [CrossRef] - Chang, J.; Dommer, M.; Chang, C.; Lin, L. Piezoelectric nanofibres for energy scavenging applications. Nano Energy
**2012**, 1, 356–371. [Google Scholar] [CrossRef] - Lugovaya, M.A.; Naumenko, A.A.; Rybyanets, A.N.; Shcherbinin, S.A. Complex material properties of porous piezoelectric ceramics. Ferroelectrics
**2015**, 484, 87–94. [Google Scholar] [CrossRef] - Sun, C.; Shi, J.; Bayerl, D.J.; Wang, X. PVDF microbelts for harvesting energy from respiration. Energy Environ. Sci.
**2011**, 4, 4508–4512. [Google Scholar] [CrossRef] - Vatansever, D.; Hadimani, R.L.; Shah, T.; Siores, E. An investigation of energy harvesting from renewable source with PVDF and PZT. Smart Mater. Struct.
**2011**, 20, 055019. [Google Scholar] [CrossRef] - Patel, I.; Siores, E.; Shah, T. Utilisation of smart polymers and ceramic based piezoelectric materials for scavenging waste energy. Sens. Actuators A: Phys.
**2010**, 159, 213–218. [Google Scholar] [CrossRef] - Anton, S.R.; Farinholt, K.M. An evaluation on low-level vibration energy harvesting using piezoelectret foam. Proc. SPIE. Act. Passiv. Smart Struct. Integr. Syst.
**2012**, 8341, 83410G. [Google Scholar] [CrossRef] - Qi, Y.; Jafferis, N.T.; Lyons, K., Jr.; Lee, C.M.; Ahmad, H.; McAlpine, M.C. Piezoelectric ribbons printed onto rubber for flexible energy conversion. Nano Lett.
**2010**, 10, 524–525. [Google Scholar] [CrossRef][Green Version] - Qi, Y.; Nguyen, T.D.; Lisko, B.; Purohit, P.K.; McAlpine, C.M. Enhanced piezoelectricity and stretchability in energy harvesting devices fabricated from buckled PZT ribbons. Nano Lett.
**2011**, 11, 1331–1336. [Google Scholar] [CrossRef] - Nguyen, T.D.; Deshmukh, N.; Nagarah, J.M.; Kramer, T.; Purohit, P.K.; Berry, M.J.; McAlpine, M.C. Piezoelectric nanoribbons for monitoring cellular deformations. Nat. Nanotechnol.
**2012**, 7, 587–593. [Google Scholar] [CrossRef] - Lee, B.Y.; Zhang, J.; Zueger, C.; Chung, W.-J.; Yoo, S.Y.; Wang, E.; Meyer, J.; Ramesh, R.; Lee, S.-W. Virus-based piezoelectric energy generation. Nat. Nanotechnol.
**2012**, 7, 351–356. [Google Scholar] [CrossRef] [PubMed] - Rybyanets, A.N. Advanced functional materials: Modeling, technology, characterization, and applications. In Advanced Materials. Manufacturing, Physics, Mechanics and Applications. Springer Proceedings in Physics; Parinov, I., Chang, S.H., Topolov, V., Eds.; Springer: Cham, Switzerland, 2016; Volume 175, pp. 211–228. [Google Scholar] [CrossRef]
- Shvetsova, N.A.; Lugovaya, M.A.; Shvetsov, I.A.; Makariev, D.I.; Rybyanets, A.N. Dielectric, piezoelectric and elastic properties of PZT/PZT ceramic piezocomposites. In Physics, Mechanics of New Materials and Their Applications; Parinov, I.A., Chang, S.H., Topolov, V.Y., Eds.; Nova Science Publishers: Hauppauge, NY, USA, 2016; pp. 407–414. Available online: https://novapublishers.com/shop/proceedings-of-the-2015-international-conference-on-physics-mechanics-of-new-materials-and-their-applications-devoted-to-the-100th-anniversary-of-the-southern-federal-university/ (accessed on 2 April 2022).
- Newnham, R.E. Fifty years of ferroelectrics. In Proceedings of the 14th IEEE International Symposium on Applications of Ferroelectrics (ISAF-04), Montréal, QC, Canada, 23–27 August 2004; pp. 1–6. [Google Scholar]
- Rybyanets, A.N. Ceramic piezocomposites: Modeling, technology, and characterization. In Piezoceramic Materials and Devices; Parinov, I.A., Ed.; Nova Science Publishers: Hauppauge, NY, USA, 2010; pp. 113–174. Available online: http://www.novapublishers.org/catalog/product_info.php?products_id=11605 (accessed on 2 April 2022).
- Nasedkin, A.V. Computer design of porous active materials at different dimensional scales. AIP Conf. Proc.
**2017**, 1909, 020145. [Google Scholar] [CrossRef] - Nasedkin, A.V.; Shevtsova, M.S. Improved finite element approaches for modeling of porous piezocomposite materials with different connectivity. In Ferroelectrics and Superconductors: Properties and Applications; Parinov, I.A., Ed.; Nova Science Publishers: Hauppauge, NY, USA, 2012; pp. 231–254. Available online: http://www.novapublishers.org/catalog/product_info.php?products_id=24233 (accessed on 2 April 2022).
- Nasedkin, A.V.; Shevtsova, M.S. Multiscale computer simulation of piezoelectric devices with elements from porous piezoceramics. In Physics and Mechanics of New Materials and Their Applications; Parinov, I., Chang, S.H., Eds.; Nova Science Publishers: Hauppauge, NY, USA, 2013; pp. 185–202. Available online: https://novapublishers.com/shop/physics-and-mechanics-of-new-materials-and-their-applications/.
- Naumenko, A.A.; Lugovaya, M.A.; Shcherbinin, S.A.; Rybyanets, A.N. Elastic losses and dispersion in ceramic matrix composites. Ferroelectrics
**2015**, 484, 69–77. [Google Scholar] [CrossRef] - Rybyanets, A.N. Porous piezoelectric ceramics?A historical overview. Ferroelectrics
**2011**, 419, 90–96. [Google Scholar] [CrossRef] - Rybyanets, A.N. Porous piezoceramics: Theory, technology, and properties. IEEE Trans. Ultrason. Ferroelectr. Freq. Control
**2011**, 58, 1492–1507. [Google Scholar] [CrossRef] - Rybyanets, A.; Naumenko, A. Nanoparticles transport in ceramic matrixes: A novel approach for ceramic matrix composites fabrication. J. Mod. Phys.
**2013**, 4, 1041–1049. [Google Scholar] [CrossRef][Green Version] - Rybyanets, A.N.; Naumenko, A.A. Elastic losses and spatial dispersion in porous piezoceramics and ceramic matrix composites. In Advanced Materials—Studies and Applications; Parinov, I.A., Chang, S.H., Theerakulpisut, S., Eds.; Nova Science Publishers: Hauppauge, NY, USA, 2015; pp. 125–146. Available online: https://novapublishers.com/shop/advanced-materials-studies-and-applications/ (accessed on 2 December 2021).
- Rybyanets, A.; Rybyanets, A. Ceramic piezocomposites: Modeling, technology, and characterization. IEEE Trans. Ultrason. Ferroelectr. Freq. Control
**2011**, 58, 1757–1773. [Google Scholar] [CrossRef] - Rybyanets, A.N.; Naumenko, A.A.; Lugovaya, M.A.; Shvetsova, N.A. Electric power generations from PZT composite and porous ceramics for energy harvesting devices. Ferroelectrics
**2015**, 484, 95–100. [Google Scholar] [CrossRef] - Rybyanets, A.N.; Zaharov, Y.N.; Raevskii, I.P.; Akopjan, V.A.; Rozhkov, E.V.; Parinov, I.A. Development of new piezoelectric materials and transducer designs for energy harvesting devices. In Physics and Mechanics of New Materials and Their Applications; Parinov, I., Chang, S.H., Eds.; Nova Science Publishers: Hauppauge, NY, USA, 2013; pp. 275–308. Available online: https://novapublishers.com/shop/physics-and-mechanics-of-new-materials-and-their-applications/ (accessed on 2 April 2022).
- Andryushin, K.P.; Andryushina, I.N.; Cherpakov, A.V.; Popov, A.V.; Verbenko, I.A.; Reznichenko, L.A. Features of the electrophysical and mechanical properties of n-component ferroactive solid solutions of composition PZT–PZN–PMN. J. Adv. Dielectr.
**2021**, 11, 2160001. [Google Scholar] [CrossRef] - Nasedkin, A.; Nasedkina, A.; Rybyanets, A. Finite element simulation of effective properties of microporous piezoceramic material with metallized pore surfaces. Ferroelectrics
**2017**, 508, 100–107. [Google Scholar] [CrossRef] - Nasedkin, A.; Nassar, M.E. Effective properties of a porous inhomogeneously polarized by direction piezoceramic material with full metalized pore boundaries: Finite element analysis. J. Adv. Dielectr.
**2020**, 10, 2050018. [Google Scholar] [CrossRef] - Nasedkin, A.; Nassar, M.E. Numerical investigation of the effects of partial metallization at the pore surface on the effective properties of a porous piezoceramic composite. J. Adv. Dielectr.
**2021**, 11, 2160009. [Google Scholar] [CrossRef] - Benasciutti, D.; Moro, L.; Zelenika, S.; Brusa, E. Vibration energy scavenging via piezoelectric bimorphs of optimized shapes, Microsyst. Technol.
**2010**, 16, 657–668. [Google Scholar] [CrossRef] - Dietl, J.M.; Garcia, E. Beam shape optimization for power harvesting. J. Intell. Mater. Syst. Struct.
**2010**, 21, 633–646. [Google Scholar] [CrossRef] - Friswell, M.I.; Adhikari, S. Sensor shape design for piezoelectric cantilever beams to harvest vibration energy. J. Appl. Phys.
**2010**, 108, 014901. [Google Scholar] [CrossRef][Green Version] - Paquin, S.; St-Amant, Y. Improving the performance of a piezoelectric energy harvester using a variable thickness beam. Smart Mater. Struct.
**2010**, 19, 105020. [Google Scholar] [CrossRef] - Wang, L. Design, Fabrication and Experimental Analysis of Piezoelectric Energy Harvesters with Non-Traditional Geometries. Ph.D. Thesis, Rutgers University, New Brunswick, NJ, USA, 2011. [Google Scholar]
- Park, J.; Lee, S.; Kwak, B.M. Design optimization of piezoelectric energy harvester subject to tip excitation. J. Mech. Sci. Technol.
**2012**, 26, 137–143. [Google Scholar] [CrossRef] - Gonsalez, C.G.; Shiki, S.B.; Brennan, M.J.; Da Silva, D.; Juni, V.L. Piezoelectric energy harvesting system optimization. In Proceedings of the 2nd International Conference on Engineering Optimization, Lisbon, Portugal, 6–9 September 2010; pp. 1–8. [Google Scholar]
- Benkhelifa, E.; Moniri, M.; Tiwari, A.; De Rueda, A.G. Evolutionary multi-objective design optimisation of energy harvesting MEMS: The case of a piezoelectric. In Proceedings of the 2011 IEEE Congress of evolutionary computation (CEC 2011), New Orleans, LA, USA, 5–8 June 2011; pp. 1856–1863. [Google Scholar] [CrossRef]
- Bourisli, R.I.; Al-Ajmi, M.A. Optimization of smart beams for maximum modal electromechanical coupling using genetic algorithms. J. Intell. Mater. Syst. Struct.
**2010**, 21, 907–914. [Google Scholar] [CrossRef] - Hadas, Z.; Kurfurst, J.; Ondrusek, C.; Singule, V. Artificial intelligence based optimization for vibration energy harvesting applications. Microsyst. Technol.
**2012**, 18, 1003–1014. [Google Scholar] [CrossRef] - Dunning, P.D.; Kim, H.A. A new method for creating holes in level-set function based topology optimisation. Int. J. Numer. Methods Eng.
**2013**, 93, 118–134. [Google Scholar] [CrossRef][Green Version] - Chen, S.; Gonella, S.; Chen, W.; Liu, W.K. A level set approach for optimal design of smart energy harvesters. Comput. Methods Appl. Mech. Eng.
**2010**, 199, 2532–2543. [Google Scholar] [CrossRef] - Sun, K.H.; Kim, Y.Y. Layout design optimization for magneto-electro-elastic laminate composites for maximized energy conversion under mechanical loading. Smart Mater. Struct.
**2010**, 19, 055008. [Google Scholar] [CrossRef] - Kim, J.E.; Kim, D.S.; Kim, Y.Y. Multi-physics interpolation for the topology optimization of piezoelectric systems. Computer Methods in Appl. Mech. Eng.
**2010**, 199, 3153–3168. [Google Scholar] [CrossRef] - Noh, J.Y.; Yoon, G.H. Topology optimization of piezoelectric energy harvesting devices considering static and harmonic dynamic loads. Adv. Eng. Softw.
**2012**, 53, 45–60. [Google Scholar] [CrossRef] - Vatanabe, S.L.; Paulino, G.H.; Silva, E.C.N. Influence of pattern gradation on the design of piezocomposite energy harvesting devices using topology optimization. Compos. Pt B
**2012**, 43, 2646–2654. [Google Scholar] [CrossRef] - Lin, Z.Q.; Gea, H.C.; Liu, S.T. Design of piezoelectric energy harvesting devices subjected to broadband random vibrations by applying topology optimization. Acta Mech. Sin.
**2011**, 27, 730–737. [Google Scholar] [CrossRef] - Wein, F.; Kaltenbacher, M.; Stingl, M. Topology optimization of a cantilevered piezoelectric energy harvester using stress norm constraints. Struct. Multidiscip. Optim.
**2013**, 48, 173–185. [Google Scholar] [CrossRef] - Hehn, T.; Manoli, Y. Efficient Power Extraction, Interface Modeling and Loss Analysis, Springer Series in Advanced Microelectronics; Springer: Cham, Switzerland, 2015; Volume 38. [Google Scholar] [CrossRef]
- Wang, D.-A.; Liu, N.-Z. A shear mode piezoelectric energy harvester based on a pressurized water flow. Sens. Actuators A Phys.
**2011**, 2011 167, 449–458. [Google Scholar] [CrossRef] - Nechibvute, A.; Akande, A.R.; Luhanga, P.V.C. Modelling of a PZT Beam for Voltage Generation. Pertanika J. Sci. Technol.
**2011**, 19, 259–271. Available online: http://www.pertanika.upm.edu.my/pjst/browse/regular-issue?article=JST-0163-2009. - Lin, J.-T.; Lee, B.; Alphenaar, B. The magnetic coupling of a piezoelectric cantilever for enhanced energy harvesting efficiency. Smart Mater. Struct.
**2010**, 19, 045012. [Google Scholar] [CrossRef] - Rezaei-Hosseinabadi, N.; Tabesh, A.; Dehghani, R.; Aghili, A. An efficient piezoelectric windmill topology for energy harvesting from low-speed air flows. IEEE Trans. Ind. Electron.
**2015**, 62, 3576–3583. [Google Scholar] [CrossRef] - Kishore, R.A.; Vučković, D.; Priya, S. Ultra-low wind speed piezoelectric windmill. Ferroelectrics
**2014**, 460, 98–107. [Google Scholar] [CrossRef] - Zhang, J.; Fang, Z.; Shu, C.; Zhang, J.; Zhang, Q.; Li, C. A rotational piezoelectric energy harvester for efficient wind energy harvesting. Sens. Actuators A: Phys.
**2017**, 262, 123–129. [Google Scholar] [CrossRef] - Sirohi, J.; Mahadik, R. Harvesting Wind Energy Using a Galloping Piezoelectric Beam. J. Vib. Acoust.
**2012**, 134, 011009. [Google Scholar] [CrossRef] - Mineto, A.T.; Souza Braun, M.P.; Navarro, H.A.; Varoto, P.S. Modeling and simulation of a piezoelectric cantilever beam for power harvesting generation. In Proceedings of the 9th Brazilian Conference on Dynamics Control and their Applications (Dincon’10), São Paulo, Brazil, 7–11 June 2010; pp. 599–605. Available online: http://arquivo.sbmac.org.br/dincon/trabalhos/PDF/acoustics/67775.pdf (accessed on 2 December 2021).
- Wu, N.; Wang, Q.; Xie, X. Wind energy harvesting with a piezoelectric harvester. Smart Mater. Struct.
**2013**, 22, 095023. [Google Scholar] [CrossRef] - Zhou, S.; Cao, J.; Erturk, A.; Lin, J.; Zhou, S.; Cao, J.; Erturk, A.; Lin, J. Enhanced broadband piezoelectric energy harvesting using rotatable magnets. Appl. Phys. Lett.
**2013**, 102, 173901. [Google Scholar] [CrossRef][Green Version] - Yang, J.; Wen, Y.; Li, P.; Bai, X.; Li, M. Improved piezoelectric multifrequency energy harvesting by magnetic coupling. Proc. IEEE Sens.
**2011**, 2011, 28–31. [Google Scholar] [CrossRef] - Manla, G.; White, N.M.; Tudor, M.J. Numerical Model of a Non-Contact Piezoelectric Energy Harvester for Rotating Objects, IEEE Sens. J.
**2012**, 12, 1785–1793. [Google Scholar] [CrossRef] - Sang, Y.; Huang, X.; Liu, H.; Jin, P. A vibration-based hybrid energy harvester for wireless sensor systems. IEEE Trans. Magn.
**2012**, 48, 4495–4498. [Google Scholar] [CrossRef] - Zhou, L.; Sun, J.; Zheng, X.J.; Deng, S.F.; Zhao, J.H.; Peng, S.T.; Zhang, Y.; Wang, X.Y.; Cheng, H.B. A model for the energy harvesting performance of shear mode piezoelectric cantilever. Sens. Actuators A Phys.
**2012**, 179, 185–192. [Google Scholar] [CrossRef] - Khameneifar, F.; Arzanpour, S.; Moallem, M. A piezoelectric energy harvester for rotary motion applications: Design and experiments. J. Mechatron. IEEE/ASME Trans.
**2013**, 18, 1527–1534. [Google Scholar] [CrossRef] - Weinstein, L.A.; Cacan, M.R.; So, P.M.; Wright, P.K. Vortex shedding induced energy harvesting from piezoelectric materials in heating, ventilation and air conditioning flows. Smart Mater. Struct.
**2012**, 21, 045003. [Google Scholar] [CrossRef] - Tao, J.X.; Viet, N.V.; Carpinteri, A.; Wang, Q. Energy harvesting from wind by a piezoelectric harvester. Eng. Struct.
**2017**, 133, 74–80. [Google Scholar] [CrossRef] - Viet, N.V.; Al-Qutayri, M.; Liew, K.M.; Wang, Q. An octo-generator for energy harvesting based on the piezoelectric effect. Appl. Ocean Res.
**2017**, 64, 128–134. [Google Scholar] [CrossRef] - Xie, X.D.; Wang, Q.; Wu, N. A ring piezoelectric energy harvester excited by magnetic forces. Int. J. Eng. Sci.
**2014**, 77, 71–78. [Google Scholar] [CrossRef] - Zheng, X.; Zhang, Z.; Zhu, Y.; Mei, J.; Peng, S.; Li, L.; Yu, Y. Analysis of Energy Harvesting Performance for Mode Piezoelectric Bimorph in Series Connection Based on Timoshenko Beam Model. IEEE/ASME Trans. Mechatron.
**2015**, 20, 728–739. [Google Scholar] [CrossRef] - Rödig, T.; Schönecker, A.; Gerlach, G. A Survey on Piezoelectric Ceramics for Generator Application. J. Am. Ceram. Soc.
**2010**, 93, 901–912. [Google Scholar] [CrossRef] - Narolia, T.; Gupta, V.K.; Parinov, I.A. On Extraction of Energy from Rotating Objects. In Advanced Materials. Springer Proceedings in Materials; Parinov, I., Chang, S.H., Long, B., Eds.; Springer: Cham, Switzerland, 2020; Volume 6, pp. 503–511. [Google Scholar] [CrossRef]
- Narolia, T.; Gupta, V.K.; Parinov, I.A. A. A Novel Design for Piezoelectric Based Harvester for Rotating Objects. In Advanced Materials. Springer Proceedings in Physics; Parinov, I., Chang, S.H., Kim, Y.H., Eds.; Springer: Cham, Switzerland, 2019; Volume 224, pp. 603–614. [Google Scholar] [CrossRef]
- Narolia, T.; Gupta, V.K.; Parinov, I.A. A. A Scissor Mechanism Shear Mode Piezoelectric Energy Harvester for Windmill. In Physics and Mechanics of New Materials and Their Applications. PHENMA 2021. Springer Proceedings in Materials; Parinov, I.A., Chang, S.H., Kim, Y.H., Noda, N.A., Eds.; Springer: Cham, Switzerland, 2021; Volume 10, pp. 495–509. [Google Scholar] [CrossRef]
- Narolia, T.; Gupta, V.K.; Parinov, I.A. Design and analysis of a shear mode piezoelectric energy harvester for rotational motion system. J. Adv. Dielectr.
**2020**, 10, 2050008. [Google Scholar] [CrossRef] - Deng, Q.; Kammoun, M.; Erturk, A.; Sharma, P. Nanoscale flexoelectric energy harvesting. Int. J. Solids Struct.
**2014**, 51, 3218–3225. [Google Scholar] [CrossRef][Green Version] - Li, A.; Zhao, W.; Zhou, S.; Wang, L.; Zhang, L. Enhanced energy harvesting of cantilevered flexoelectric micro-beam by proof mass. AIP Adv.
**2019**, 9, 115305. [Google Scholar] [CrossRef] - Li, Z.; Deng, Q.; Shen, S. Flexoelectric Energy Harvesting Using Circular Thin Membranes. J. Appl. Mech.
**2020**, 87, 091004. [Google Scholar] [CrossRef] - Liang, X.; Zhang, R.; Hu, S.; Shen, S. Flexoelectric energy harvesters based on Timoshenko laminated beam theory. J. Intell. Mater. Syst. Struct.
**2017**, 28, 2064–2073. [Google Scholar] [CrossRef] - Lutokhin, A.G.; Bikyashev, E.A.; Zakharov, Y.N.; Reshetnikova, E.A.; Raevskii, I.P.; Korchagin, N.A. A comprehensive investigation of phase transformations in the Pb
_{0.9975}[Zr_{0.495}Sn_{0.4}Ti_{0.1}Nb_{0.005}]O_{3}ceramics. Phys. Solid State**2012**, 54, 1021–1025. [Google Scholar] [CrossRef] - Sakhnenko, V.P.; Zakharov, Y.N.; Lutokhin, A.G.; Parinov, I.; Filatova, N.S.; Raevski, I.; Chebanenko, V.A.; Rozhkov, E.; Pavlenko, A.V.; Bunin, M.A.; et al. Studies of the unipolarity arising in the non-poled ferroelectric ceramics with electrodes from different metals on the opposite sides. Ferroelectrics
**2018**, 525, 187–191. [Google Scholar] [CrossRef] - Sakhnenko, V.P.; Zakharov, Y.N.; Parinov, I.A.; Lutokhin, A.G.; Rozhkov, E.V.; Filatova, N.S.; Raevski, I.P.; Chebanenko, V.A.; Pavlenko, A.V.; Kiseleva, L.I.; et al. Electric response to bending vibrations and pyroelectric effect in unpolarized ferroelectric ceramic plates with electrodes, differing in the magnitude of the coefficient of thermal expansion on opposite surfaces. In Advanced Materials. PHENMA 2017. Springer Proceedings in Physics; Parinov, I., Chang, S.H., Gupta, V., Eds.; Springer: Cham, Switzerland, 2018; Volume 207, pp. 161–169. [Google Scholar] [CrossRef]
- Zakharov, Y.N.; Sakhnenko, V.P.; Parinov, I.A.; Raevsky, I.P.; Bunin, M.A.; Chebanenko, V.A.; Zaerko, M.A.; Sitalo, E.I.; Pavelko, A.A.; Kiseleva, L.I. Possibilities of the practical use of a stationary strain gradient in the interelectrode volume of unpolarized ferroceramic plates. J. Adv. Dielectr.
**2020**, 10, 2060010. [Google Scholar] [CrossRef] - Zakharov, Y.N.; Sakhnenko, V.P.; Raevsky, I.P.; Parinov, I.A.; Bunin, M.A.; Raevskaya, S.I.; Chebanenko, V.A.; Filatova, N.S.; Aleshin., V.A.; Sitalo, E.I. Method for Polarization of Ferroelectric Ceramic. Russian Patent for Invention RU 2717164 C1, 18 March 2020. Application No. 2019132704 dated 16.10.2019. Available online: https://elibrary.ru/item.asp?id=42588001 (accessed on 2 December 2021). (In Russian).
- Abdollahi, A.; Peco, C.; Millán, D.; Arroyo, M.; Arias, I. Computational evaluation of the flexoelectric effect in dielectric solids. J. Appl. Phys.
**2014**, 116, 093502. [Google Scholar] [CrossRef] - Hu, S.L.; Shen, S.P. Variational principles and governing equations in nano-dielectrics with the flexoelectric effect. Sci. China Phys. Mech. Astron.
**2010**, 53, 1497–1504. [Google Scholar] [CrossRef] - Mindlin, R.D. On the Equations of Motion of Piezoelectric Crystals. In Problems of Continuum Mechanics; Muskilishivili, N.I., Ed.; 70th Birthday Volume; SIAM: Philadelphia, PA, USA, 1961; pp. 282–290. [Google Scholar]
- Chebanenko, V.A. Investigation of Oscillations of Piezoelectric Structures in the Composition of Energy Harvesting Devices. Ph.D. Thesis, Southern Federal University, Rostov-on-Don, Russia, 2018. (In Russian). [Google Scholar]
- Soloviev, A.N.; Chebanenko, V.A.; Zakharov, Y.N.; Rozhkov, E.V.; Parinov, I.A.; Gupta, V.K. Study of the Output Characteristics of Ferroelectric Ceramic Beam Made from Non-polarized Ceramics PZT-19: Experiment and Modeling. In Advanced Materials. Springer Proceedings in Physics; Parinov, I.A., Chang, S.H., Jani, M., Eds.; Springer: Cham, Switzerland, 2017; Volume 193, pp. 485–499. [Google Scholar] [CrossRef]
- Soloviev, A.N.; Vernigora, G.D. Identification of effective properties of the piezocomposites on the base of FEM modeling with ACELAN. In Piezoceramic Materials and Devices; Parinov, I., Ed.; Nova Science Publishers: Hauppauge, NY, USA, 2010; pp. 219–242. Available online: http://www.novapublishers.org/catalog/product_info.php?products_id=11605 (accessed on 2 April 2022).
- Soloviev, A.N.; Chebanenko, V.A.; Parinov, I.A.; Oganesyan, P.A. Applied theory of bending vibrations of a piezoelectric bimorph with a quadratic electric potential distribution. Mater. Phys. Mech.
**2019**, 42, 65–73. [Google Scholar] [CrossRef] - Liu, H.; Huang, Z.; Xu, T.; Chen, D. Enhancing output power of a piezoelectric cantilever energy harvester using an oscillator. Smart Mater. Struct.
**2012**, 21, 065004. [Google Scholar] [CrossRef] - Hao, W.; Lihua, T.; Yaowen, Y.; Chee, K.S. Development of a broadband nonlinear two-degree-of-freedom piezoelectric energy harvester. J. Intell. Mater. Syst. Struct.
**2014**, 25, 1875–1889. [Google Scholar] [CrossRef] - Wu, H.; Tang, L.; Yang, Y.; Soh, C.K. A novel two-degrees-of-freedom piezoelectric energy harvester. J. Intell. Mater. Syst. Struct.
**2013**, 24, 357–368. [Google Scholar] [CrossRef] - Rguiti, M.; Hajjaji, A.; D’Astorg, S.; Courtois, C.; Leriche, A. Elaboration and characterization of a low frequency and wideband piezoceramic generator for energy harvesting. Opt. Mater.
**2013**, 36, 8. [Google Scholar] [CrossRef] - Lim, J.-H.; Jeong, S.-S.; Kim, N.-R.; Cheon, S.-K.; Kim, M.-H.; Park, T.-G. Design and fabrication of a cross-shaped piezoelectric generator for energy harvesting. Ceram. Int.
**2013**, 39, S641–S645. [Google Scholar] [CrossRef] - Lim, J.-H.; Park, C.-H.; Kim, J.-W.; Jeong, S.-S.; Kim, M.-H.; Park, T.-G. Generating characteristics of a cross-shaped piezoelectric generator depending on elastic body material and leg length. J. Electroceramics
**2013**, 30, 108–112. [Google Scholar] [CrossRef] - Park, J.C.; Park, J.Y. Asymmetric PZT bimorph cantilever for multi-dimensional ambient vibration harvesting. Ceram. Int.
**2013**, 39, S653–S657. [Google Scholar] [CrossRef] - Bibo, A.; Li, G.; Daqaq, M.F. Electromechanical modeling and normal form analysis of an aeroelastic micro-power generator. J. Intell. Mater. Syst. Struct.
**2011**, 22, 577–592. [Google Scholar] [CrossRef] - Michelin, S.; Doaré, D. Energy harvesting efficiency of piezoelectric flags in axial flows. J. Fluid Mech.
**2013**, 714, 489–504. [Google Scholar] [CrossRef][Green Version] - Bibo, A.; Daqaq, M.F. Investigation of concurrent energy harvesting from ambient vibrations and wind using a single piezoelectric generator. Applied Physics Letters
**2013**, 102, 243904. [Google Scholar] [CrossRef][Green Version] - Abdelkefi, A.; Nayfeh, A.H.; Hajj, M.R. Design of piezoaeroelastic energy harvesters. Nonlinear Dyn.
**2012**, 68, 519–530. [Google Scholar] [CrossRef] - Nechibvute, A.; Chawanda, A.; Luhanga, P.; Akande, A. Piezoelectric Energy Harvesting Using Synchronized Switching Techniques. Int. J. Eng. Technol.
**2012**, 2, 936–945. [Google Scholar] - Reilly, E.K.; Burghardt, F.; Fain, R.; Wright, P. Powering a wireless sensor node with a vibration-driven piezoelectric energy harvester. Smart Mater. Struct.
**2011**, 20, 125006. [Google Scholar] [CrossRef] - Akopyan, V.A.; Zakharov, Y.N.; Parinov, I.A.; Rozhkov, E.V.; Shevtsov, S.N.; Wu, P.C.; Wu, J.K. Theoretical and Experimental Investigations of Piezoelectric Generators of Various Types. In Physics and Mechanics of New Materials and Their Applications; Parinov, I., Chang, S.H., Eds.; Nova Science Publishers: Hauppauge, NY, USA, 2013; pp. 309–334. Available online: https://novapublishers.com/shop/physics-and-mechanics-of-new-materials-and-their-applications/ (accessed on 2 April 2022).
- Parinov, I.A.; Cherpakov, A.V.; Rozhkov, E.V.; Soloviev, A.N.; Chebanenko, V.A. Program-signal generator “Sgenerator” RU 2018610408, 10 January 2018. Application No. 2017661586 dated 11/13/2017. Available online: https://elibrary.ru/item.asp?id=39279218 (accessed on 2 December 2021). (In Russian).
- Parinov, I.A.; Soloviev, A.N.; Cherpakov, A.V. The program “Vibrograf” for registration, visualization and processing of vibrations of structures RU 2016612309, 24 February 2016. Application No. 2015663157 dated 12/30/2015. Available online: https://elibrary.ru/item.asp?id=39344305 (accessed on 2 December 2021). (In Russian).
- Chebanenko, V.A.; Zhilyaev, I.V.; Soloviev, A.N.; Cherpakov, A.V.; Parinov, I.A. Numerical optimization of the piezoelectric generators. J. Adv. Dielectr.
**2020**, 10, 2060016. [Google Scholar] [CrossRef] - Cherpakov, A.V.; Kokareva, Y.A. Modal analysis of the cantilever type piezo-electric generator characteristics with active based on numerical simulation. IOP Conf. Ser. Mater. Sci. Eng.
**2019**, 698, 066020. [Google Scholar] [CrossRef] - Cherpakov, A.V.; Parinov, I.A.; Soloviev, A.N.; Rozhkov, E.V. Experimental Studies of Cantilever Type PEG with Proof Mass and Active Clamping. In Advanced Materials. Springer Proceedings in Physics; Parinov, I., Chang, S.H., Kim, Y.H., Eds.; Springer: Cham, Switzerland, 2019; Volume 224, pp. 593–601. [Google Scholar] [CrossRef]
- Polyakova, T.V.; Cherpakov, A.V.; Parinov, I.A.; Grigoryan, M.N. Estimation of the output parameters of a numerical model of a cantilever-type piezoelectric generator with attached mass and active termination upon pulsed excitation. IOP Conf. Ser. Mater. Sci. Eng.
**2020**, 913, 022014. [Google Scholar] [CrossRef] - Soloviev, A.N.; Chebanenko, V.A.; Zhilyaev, I.V.; Cherpakov, A.V.; Parinov, I.A. Numerical optimization of the cantilever piezoelectric generator. Mater. Phys. Mech.
**2020**, 44, 94–102. [Google Scholar] [CrossRef] - Soloviev, A.N.; Parinov, I.A.; Cherpakov, A.V.; Chayka, Y.A.; Rozhkov, E.V. Analysis of Oscillation Forms at Defect Identification in Node of Truss Based on Finite Element Modeling. Mater. Phys. Mech.
**2018**, 37, 192–197. [Google Scholar] [CrossRef] - Iovane, G.; Nasedkin, A.V. Finite element modelling of ceramomatrix piezocomposites by using effective moduli method with different variants of boundary conditions. Materials. Physics. Mech.
**2019**, 42, 1–13. [Google Scholar] - Iyer, S.; Venkatesh, T.A. Electromechanical response of (3-0, 3-1) particulate, fibrous, and porous piezoelectric composites with anisotropic constituents: A model based on the homogenization method. Int. J. Solids Struct.
**2014**, 51, 1221–1234. [Google Scholar] [CrossRef][Green Version] - Soloviev, A.N.; Parinov, I.A.; Cherpakov, A.V. Modeling the Cantilever Type PEG with Proof Mass and Active Pinching by Using the Porous Piezoceramics with Effective Properties. In Physics and Mechanics of New Materials and Their Applications. PHENMA 2020. Springer Proceedings in Materials; Parinov, I.A., Chang, S.H., Kim, Y.H., Noda, N.A., Eds.; Springer: Cham, Switzerland, 2021; Volume 10, pp. 481–493. [Google Scholar] [CrossRef]
- Nasedkin, A.V. Finite-Element Modeling of Piezoelectric Generators from Highly Porous Piezoceramics; Institute of Hydromechanics, National Academy of Science: Kiev, Ukraine, 2011. [Google Scholar]
- Nasedkin, A.V. Finite Element Design of Piezoelectric and Magnetoelectric Composites with Use of Symmetric Quasidefinite Matrices. In Advanced Materials—Studies and Applications; Parinov, I.A., Chang, S.H., Theerakulpisut, S., Eds.; Nova Science Publishers: Hauppauge, NY, USA, 2015; pp. 109–124. Available online: https://novapublishers.com/shop/advanced-materials-studies-and-applications/ (accessed on 2 April 2022).
- Stanton, S.C.; McGehee, C.C.; Mann, B.P. Nonlinear dynamics for broadband energy harvesting: Investigation of a bistable piezoelectric inertial generator. Physica D: Nonlinear Phenom.
**2010**, 239, 640–653. [Google Scholar] [CrossRef] - Nechibvute, A.; Chawanda, A.; Luhanga, P. Finite Element Modeling of a Piezoelectric Composite Beam and Comparative Performance Study of Piezoelectric Materials for Voltage Generation. ISRN Mater. Sci.
**2012**, 921361. [Google Scholar] [CrossRef][Green Version] - Solovyev, A.N.; Duong, L.V. Optimization for the Harvesting Structure of the Piezoelectric Bimorph Energy Harvesters Circular Plate by Reduced Order Finite Element Analysis. Int. J. Appl. Mech.
**2016**, 8, 1650029. [Google Scholar] [CrossRef] - Stewart, M.; Weaver, P.M.; Cain, M. Charge redistribution in piezoelectric energy harvesters. Appl. Phys. Lett.
**2012**, 100, 073901. [Google Scholar] [CrossRef] - Tang, L.; Yang, Y.; Soh, C.K. Broadband vibration energy harvesting techniques. In Advances in Energy Harvesting Methods; Elvin, N., Erturk, A., Eds.; Springer: Berlin/Heidelberg, Germany, 2013; pp. 17–61. [Google Scholar] [CrossRef]
- Zhu, D.; Tudor, M.J.; Beeby, S.P. Strategies for increasing the operating frequency range of vibration energy harvesters: A review. Meas. Sci. Technol.
**2010**, 21, 022001. [Google Scholar] [CrossRef] - Karami, M.A.; Inman, D.J. Powering pacemakers from heartbeat vibrations using linear and nonlinear energy harvesters. Appl. Phys. Lett.
**2012**, 100, 042901. [Google Scholar] [CrossRef] - Arrieta, A.F.; Hagedorn, P.; Erturk, A.; Inman, D.J. A piezoelectric bistable plate for nonlinear broadband energy harvesting. Appl. Phys. Lett.
**2010**, 97, 104102. [Google Scholar] [CrossRef][Green Version] - Tang, L.; Yang, Y.; Zhao, L. Magnetic Coupled Cantilever Piezoelectric Energy Harvester. Smart Mater. Adapt. Struct. Intell. Syst.
**2012**, 2, 811–818. [Google Scholar] [CrossRef] - Zhou, S.; Cao, J.; Inman, D.J.; Lin, J.; Liu, S.; Wang, Z. Broadband tristable energy harvester: Modeling and experiment verification. Appl. Energy
**2014**, 133, 33–39. [Google Scholar] [CrossRef] - Haldkar, R.K.; Parinov, I.A. Wind Energy Harvesting from Artificial Grass by using Micro Fibre Composite. In Physics and Mechanics of New Materials and Their Applications PHENMA 2021. Springer Proceedings in Materials; Parinov, I.A., Chang, S.H., Kim, Y.H., Noda, N.A., Eds.; Springer: Cham, Switzerland, 2021; Volume 10, pp. 511–518. [Google Scholar] [CrossRef]
- Gao, F.; Liu, G.; Chung, B.L.H.; Chan, H.H.T.; Liao, W.H. Macro fiber composite-based energy harvester for human knee. Appl. Phys. Lett.
**2019**, 115, 033901. [Google Scholar] [CrossRef] - Ju, S.; Chae, S.H.; Choi, Y.; Ji, C. Macro fiber composite-based low frequency vibration. energy harvester. Sens. Actuators A Phys.
**2015**, 226, 126–136. [Google Scholar] [CrossRef] - Khalatkar, A.; Gupta, V.K.; Haldkar, R. Modeling and simulation of cantilever beam for optimal placement of piezoelectric actuators for maximum energy harvesting. Proc. SPIE 8204 Smart Nano-Micro Mater. Devices
**2011**, 8204, 82042G. [Google Scholar] [CrossRef] - Khalatkar, A.M.; Haldkar, R.H.; Gupta, V.K. Finite Element Analysis of Cantilever Beam for Optimal Placement of Piezoelectric Actuator. In Proceedings of the 2nd International Conference on Mechanical, Material Engineering (ICMME 2014), Shiyan, China, 22–23 November 2014; Volume 110–116, pp. 4212–4220. [Google Scholar] [CrossRef]
- Khalatkar, A.M.; Kumar, R.; Haldkar, R.; Jhodkar, D. Arduino-Based Tuned Electromagnetic Shaker Using Relay for MEMS Cantilever Beam; Springer: Singapore, 2019. [Google Scholar]
- Orrego, S.; Shoele, K.; Ruas, A.; Doran, K.; Caggiano, B.; Mittal, R.; Kang, S.H. Harvesting ambient wind energy with an inverted piezoelectric flag. Appl. Energy
**2017**, 194, 212–222. [Google Scholar] [CrossRef] - Lai, Z.; Wang, S.; Zhu, L.; Zhang, G.; Wang, J.; Yang, K.; Yurchenko, D. A hybrid piezo-dielectric wind energy harvester for high-performance vortex-induced vibration energy. Mech. Syst. Signal Processing
**2021**, 150, 107212. [Google Scholar] [CrossRef] - Liu, J.; Chen, X.; Chen, Y.; Zuo, H.; Li, Q. Experimental Research on Wind-Induced Flag-Swing Piezoelectric Energy Harvesters. Shock Vib.
**2021**, 2021, 8496441. [Google Scholar] [CrossRef] - Muñoz, C.Q.G.; Alcalde, G.Z.; Márquez, F.P.G. Analysis and Comparison of Macro Fiber Composites and Lead Zirconate Titanate (PZT) Discs for an Energy Harvesting Floor. Appl. Sci.
**2020**, 10, 5951. [Google Scholar] [CrossRef] - Wang, J.D.; Yurchenko, D.; Hu, G.; Zhao, L.; Tang, L.; Yang, Y. Perspectives in flow-induced vibration energy harvesting. Appl. Phys. Lett.
**2021**, 119, 100502. [Google Scholar] [CrossRef] - Li, X.; Guo, M.; Dong, S.A. flex-compressive-mode piezoelectric transducer for mechanical vibration/strain energy harvesting. IEEE Trans. Ultrason. Ferroelectr. Freq. Control
**2011**, 58, 698–703. [Google Scholar] [CrossRef] - Zhao, S.; Erturk, A. Energy harvesting from harmonic and noise excitation of multilayer piezoelectric stacks: Modeling and experiment. Act. Passiv. Smart Struct. Integr. Syst.
**2013**, 8688, 86881Q. [Google Scholar] [CrossRef] - Rupp, C.J.; Dunn, M.L.; Maute, K. Analysis of piezoelectric energy harvesting systems with non-linear circuits using the harmonic balance method. J. Intell. Mater. Syst. Struct.
**2010**, 21, 1383–1396. [Google Scholar] [CrossRef] - Shevtsov, S.; Flek, M.; Acopyan, V.; Samochenko, I.; Axenov, V. On the active vibration control and stability of the tubular structures by piezoelectric patch-like actuators. Math. Eng. Sci. Aerosp.
**2011**, 2, 145–157. Available online: https://www.researchgate.net/publication/267666291_On_the_active_vibration_control_and_stability_of_the_tubular_structures_by_piezoelectric_patch-like_actuators (accessed on 2 April 2022). - Wang, Y.; Inman, D.J. A survey of control strategies for simultaneous vibration suppression and energy harvesting via piezoceramics, J. Intell. Mater. Syst. Struct.
**2012**, 23, 2021–2037. [Google Scholar] [CrossRef] - Wickenheiser, A.M.; Garcia, E. Power optimization of vibration energy harvesters utilizing passive and active circuits, J. Intell. Mater. Syst. Struct.
**2010**, 21, 1343–1361. [Google Scholar] [CrossRef]

**Figure 1.**Configuration of piezoelectric energy harvester with parallel coaxial plates (from Narolia et al. [178], reproduced by permission of Springer Nature © 2022).

**Figure 2.**Configuration of energy harvester with rotating hub (from Narolia et al. [179], reproduced by permission of Springer Nature © 2022).

**Figure 3.**(

**a**) Configuration of wind turbine and (

**b**) energy harvester with scissor mechanism (from Narolia et al. [180], reproduced by permission of Springer Nature © 2022).

**Figure 4.**Configuration of energy harvester (from Narolia et al. [181], reproduced by permission of Journal of Advanced Dielectrics, Vol. 10, No. 03, @ 2020 and World Scientific Publishing Co. Pte. Ltd.).

**Figure 5.**Electrical responses of samples with applied Ag- and Pt-electrodes to the bending at the resonant frequency.

**Figure 6.**General view of the test set-up (

**a**) and its block diagram (

**b**): 1—piezoceramic beam, 2—proof mass, 3—1st fixing point, 4—base, 5—worktable of the electromagnetic shaker, 6—shaker, 7—optical linear displacement sensor, 8—optical sensor’s controller, 9—ADXL-103 acceleration sensor (located at 2nd fixing point), 10—acceleration sensor’s controller, 11—ADC/DAC E14–440D external unit, 12—power amplifier, 13—signal generator, and 14—computer; ${R}_{l}$ is the electric load resistance (from Shevtsov et al. [57], reproduced by permission of Springer Nature © 2022).

**Figure 8.**Frequency response of the voltage across the resistor with various values of the load resistance, obtained from the numerical experiment (from Shevtsov et al. [57], reproduced by permission of Springer Nature © 2022).

**Figure 9.**(

**a**) Electrical scheme of PEG at vibration loading and (

**b**) structural scheme of PEG with proof mass: 1—plate piezoelectric elements (PEs); 2—substrate; 3—proof mass; 4—PEG fixation point (with movable base b); and 5—cylindrical PE.

**Figure 10.**Vibration setup with PEG: 1—vibrating table; 2—PEG; 3—laser sensor optoNSDT of displacement; 4—support of laser sensor 3; 5—electric path of PEG; 6—triangulation laser sensor of displacements RF603; 7—sensor support stand (6); 8—cylindrical PEs, located at the base of the PEG; and 9—PE plates.

**Figure 11.**Measuring set-up: 1—PEG; 2—vibration exciter; 3—optical sensor of linear displacements optoNSDT; 4—controller of optical sensor 3; 5—optical sensor of linear displacements RF603; 6—controller of optical sensor 5; 7—external ADC/DAC module L-Card 14-440; 8—matching device of acceleration sensor; 9—power amplifier; 10—AFG3022 signal generator set or sound card; and 11—computer.

**Figure 12.**Dependence of output electric power on load resistance for various values of displacement amplitude of free tip of the cantilever at a proof mass of 20.6 g.

**Figure 13.**Experimental set-up for research of double-cantilever PEG: the numbers point out displacement measurer (1), accelerometer (2), shaker (3), and proof mass (4).

**Figure 15.**Output power (

**a**) and output voltage (

**b**) vs. active load for two locations of proof mass: L

_{m}= 65 and 103.5 mm.

**Figure 17.**Dependencies of voltage amplitude: (

**a**) for the first model; (

**a**) for the second model: 1—fiberglass; 2—duralumin; and 3—steel.

**Figure 19.**Output voltage on the (

**a**) bimorph plates, located on the PEG cantilever substrate; (

**b**) PEG piezoelectric cylinders vs. the frequency range of harmonic excitation from 0 to 600 Hz.

**Figure 20.**(

**a**) Bimorph cantilever PEG: 1 and 3—piezoelements, 2—substrate; (

**b**) cantilever-type PEG with incomplete piezoelectric coating of the substrate.

**Figure 23.**(

**a**) Biaxial PEG model with symmetrically-located proof masses; (

**b**) electric scheme of PEG under active load.

**Figure 25.**Energy harvesters from artificial grass (from Haldkar et al. [235], reproduced by permission of Springer Nature © 2022).

**Figure 27.**(

**a**) Laboratory set-up for definition of stack-type PEG characteristics: 1—screw, intended for disposition of PEG on thickness and for initial its preload, 2—immobile cross-arm, 3—test PEG sample, 4—strain-gauge dynamometer, 5—force columns, 6—directing cylinder with mobile cross-arm, 7—frequency transducer (giving frequency of the engine rotation from 10 to 1400 rpm), 8—tension amplifier, 9—transducer ADT/DAT, 10—support-bracket, 11—base, 12—eccentric disc with connecting-rod 13, 14—reduction gear, and 15—engine; (

**b**) kinematic scheme of the loading module: 1—engine, reduction gear and eccentric disc, 2—crank mechanism, 3—preloaded screw, 4—cross-arm, 5—PEG, and 6—strain-gauge dynamometer (reprinted from Chebanenko [194]).

**Figure 28.**(

**a**) Loading module of the laboratory set-up for definition of characteristics of stack-type PEG: 1—frequency transducer, giving frequency of the engine rotation from 10 to 1400 rpm; 2—engine with reduction gear and eccentric disc, and connecting-rod; 3—lever multiplier of changing compression force with transformation factor equal to 50; 4—test PEG sample; 5—strain-gauge dynamometer; and 6—support-bracket of holder; (

**b**) kinematic scheme of loading module: 1—engine, reduction gear and eccentric disc, 2—lever, 3—transforming mechanism, 4—strain-gauge dynamometer, 5—PEG, and 6—loaded screw (reprinted from Chebanenko [194]).

**Figure 29.**Shapes of piezoelectric output voltage (1–3) and pulses of compression force (4) in dependence on electric load resistance.

**Figure 30.**Output voltage (continuous curve) and output power (dotted curve) in dependence on impact frequency at various values of load resistance for the ring-type PEG with a thickness of 38 mm at a pulse mechanical load of 17.2 MPa.

**Figure 31.**Peak output power vs. PEG quasi-static loading velocity at various stack heights and electrical capacitance.

**Figure 32.**Output voltage in dependence on electric load resistance under harmonic excitation to frequency of 4 Hz at mechanical loading with value of 8.8 MPa.

**Figure 33.**Normalized output power in dependence on electric load resistance under harmonic excitation at various frequencies from 0.27 to 4 Hz.

**Figure 34.**FE model of stack-type PEG under homogeneously distributed mechanical load: (

**a**) common scheme, (

**b**) an example of modeled stack geometry, and (

**c**) FE partition of axisymmetric model (from Shevtsov et al. [77], reproduced by permission of Springer Nature © 2022).

**Figure 35.**Dependencies of the output voltage (

**a**), current (

**b**), and generated output power (

**c**) on the excitation frequency f and electric load resistance R (from Shevtsov et al. [77] reproduced by permission of Springer Nature © 2022).

**Table 1.**Comparison of electromechanical characteristics of some piezoelectrics at room temperature (from Bowen et al. [17], reproduced by permission of Springer Nature © 2022).

d_{33}, pC/N | d_{31}, pC/N | d_{15}, pC/N | k_{33} | |
---|---|---|---|---|

GaN | 3.7; 13.2 (NW) | −1.9; −9.4 (NW) | 3.1 | – |

AlN | 5.0 | −2.0 | 3.6 | 0.23 |

ZnO | 12.4; 14.3–26.7 (nanobelt) | −5.0 | −8.3 | 0.48 |

BaTiO_{3}, FC | 149 | −58 | 242 | 0.49 |

PZT-4 (hard FC) | 289 | −123 | 495 | 0.70 |

PZT-5H (soft FC) | 593 | −274 | 741 | 0.75 |

PMN–0.33PT, SC | 2820 | −1330 | 146 | 0.94 |

LiNbO_{3}, SC | 6 | −1.0 | 69 | 0.23 |

Poled PVDF | −33 | 21 | −27 | 0.19 |

_{ij}are the piezoelectric factors; and k

_{33}is the electromechanical coupling factor (ECF) at the longitudinal oscillation mode.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Parinov, I.A.; Cherpakov, A.V.
Overview: State-of-the-Art in the Energy Harvesting Based on Piezoelectric Devices for Last Decade. *Symmetry* **2022**, *14*, 765.
https://doi.org/10.3390/sym14040765

**AMA Style**

Parinov IA, Cherpakov AV.
Overview: State-of-the-Art in the Energy Harvesting Based on Piezoelectric Devices for Last Decade. *Symmetry*. 2022; 14(4):765.
https://doi.org/10.3390/sym14040765

**Chicago/Turabian Style**

Parinov, Ivan A., and Alexander V. Cherpakov.
2022. "Overview: State-of-the-Art in the Energy Harvesting Based on Piezoelectric Devices for Last Decade" *Symmetry* 14, no. 4: 765.
https://doi.org/10.3390/sym14040765