# On the Possibility of Developing Magnetostrictive Fe-Co/Ni Clad Plate with Both Vibration Energy Harvesting and Mass Sensing Elements

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## Abstract

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## 1. Introduction

_{40}Ni

_{40}P

_{14}B

_{6}) and found a linear relationship between the resonance frequency shift and the logarithm of CSFV E2 antibody concentrations ranging from 5 ng mL

^{−1}to 10 μg mL

^{−1}.

## 2. Numerical Procedure

_{1}x

_{2}x

_{3}, the governing equations are given as follows [33]:

_{ij}, B

_{i}, and u

_{i}are the stress tensor, magnetic flux density vector, and displacement vector, respectively; ρ is the mass density; and c is the damping coefficient. A comma followed by an index denotes partial differentiation with respect to the space coordinate x

_{i}or the time t, and the summation convention for repeated tensor indices is applied. The constitutive laws are given as follows [34]:

_{ij}is the strain tensor; H

_{i}is the magnetic field intensity vector; and ${s}_{ijkl}^{\mathrm{H}}$,$\text{}{d}_{kij}^{\mathrm{m}}$, and μ

_{ij}are the constant magnetic field elastic compliance, piezomagnetic constant, and magnetic permittivity, respectively. The material constants are characterized by the following symmetry conditions:

_{3}being the axis of symmetry [35]. Constitutive Equations (3) and (4) for the magnetostrictive material are given as follows:

_{0}of a thin plate with length l, width w and thickness h (h, w$\ll $l) vibrating in the longitudinal mode is given as follows [36]:

_{1}= x, x

_{2}= y, and x

_{3}= z axes, respectively. The origin of the coordinate system is located at the left-side center of the clad plate. The plate was clamped with z = 0 denoting the fixed center. The z-direction was the easy axis of magnetization for both the Fe-Co and Ni layers. The imposed base excitation was given by the displacement u

_{y}

_{0}exp(iωt) of the clamped end, where u

_{y}

_{0}is the amplitude of the applied displacement and ω = 2πf is the angular frequency. Furthermore, the mass change induced changes in the magnetic flux density and frequency of the clad plate were calculated via finite element analysis. Moreover, through Faraday’s law, the output voltage was obtained from the magnetic flux density change as follows:

## 3. Experiment

_{out}of the Fe-Co/Ni clad plate, a vibration power generation test was executed using a vibrator. The clad plate cantilever with a proof mass of m = 1, 2, 4, 7, or 10 mg was mounted on the vibration shaker (ET-132, Labworks Inc., Costa Mesa, CA, USA), and the imposed displacement vibration was applied with the shaker. The proof mass was a masking tape made of paper. A cantilever without the mass was also used. The free length of the cantilever was l = 33 mm. The peak-to-peak output voltage V

_{pp}= 2V

_{out}associated with various values of the frequency f was recorded using a data logger (NR-500 series, Keyence Corporation, Osaka, Japan). The number of turns of the coil, resistance of the coil, and the sampling period were ~4200, 7.47 kΩ, and 100 μs, respectively. Figure 2 shows the specimen and experimental setup.

## 4. Results and Discussion

_{pp}versus frequency f for the Fe-Co/Ni clad plates with a proof mass of m = 0, 1, 2, 4, 7, and 10 mg. The resonance frequency of the Fe-Co/Ni clad plate without the proof mass was ~107 Hz. It was expected that for the first mode, the maximum output voltage generated from the Fe-Co/Ni clad plate without the proof mass would be ~85 mV. As the weight of the mass increases, the frequency decreases, and the maximum output voltage increases slightly. Table 4 presents a comparison of the output voltage density of the Fe-Co/Ni clad plate with the magnetostrictive harvesters [21,25,27,29,39,40]. Although the output voltage density depends on the bias magnetic field, excitation conditions, number of coil turns, etc., the performance of the Fe-Co/Ni clad plate is almost comparable to those of other magnetostrictive harvesters. Figure 4 shows the measured and calculated frequency shift Δf (due to the proof mass) as a function of the load P or weight m of the mass. The damping ratios ζ = c/c

_{c}(c

_{c}: critical damping coefficient) of the Fe-Co/Ni clad plate with a proof mass of m = 0, 1, 2, 4, 7, and 10 mg were obtained by the half power method and were 0.0084, 0.0094, 0.0085, 0.0091, 0.0087, and 0.0094. The length L and height H of the mass were 1 mm and 0.1 mm, respectively. The frequency shift decreases linearly with increasing load or weight. In addition, the mass can be detected from changes in the resonance frequency of this clad steel plate.

_{0}of the Fe-Co/Ni clad plates where the distance between the center of the proof mass and the fixed end is a = 0.5, 9.5, 19, 28.5, and 37.5 mm. The length L and height H of the mass were 1 mm and 0.1 mm, respectively. The calculated frequency shifts Δf due to the mass of weight m = 10 mg are shown in the figure. The resonance frequency increases (as expected) with decreasing distance of the proof mass from the fixed end, whereas the frequency shift decreases. Figure 6 shows the calculated resonance frequency f

_{0}and frequency shift Δf due to the mass with weight m = 10 mg of the Fe-Co/Ni clad plates. The f

_{0}and Δf values were calculated for various values of a (the distance between the proof mass and the fixed end) and L (the length; L = 12, 4, and 1 mm) of the proof mass. When the proof mass is near the fixed end, the frequency increases with the mass as the size of the mass increases even if the weight is the same. The frequency changes only slightly when the proof mass is in the center of the cantilever. When the mass is near the free end, the frequency is reduced by the mass regardless of the mass size.

_{pp}versus the load P or weight m obtained from the experiment and finite element analysis. The voltage decreases by ~12 mV at a weight of m = 1 mg. The results shown in this figure suggest that the output voltage decreases linearly due to the mass change at the microgram level.

_{0}of the plate without antigen binding decreases to f

_{1}owing to the fact that antigen binds to the antibody immobilized on the sensor surface. This shift of the resonance frequency can be monitored by using a pickup coil. Our Fe-Co/Ni clad plate serves as the bending vibration energy harvesting device, and without antigen adsorption, the harvested power will be able to supply as a source of transmitting power in order to forward information from the sensor. Furthermore, this plate for energy harvesting is subjected to bending vibration and serves as the biosensor without the need for an AC magnetic field (see Figure 8a). In addition, our biosensor may be able to detect the mass from the reduced output voltage ΔV = V

_{0}− V

_{1}, which will significantly reduce the detection time (Figure 8b). The purpose of this study is to confirm the principles of vibration energy harvesting and mass detection. Hence, the “mass” of the mass sensing element is not specifically identified. In future research, experiments will be conducted on the mass of the virus. The comparison between two types of traditional biosensors [32,44] and our future biosensor is given in Table 5.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Bryzek, J. Proceedings of the TSensors Summit, Stanford University, Stanford, CA, USA, 23–25 October 2013.
- 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] - Wang, Z.; Narita, F. Fabrication of potassium sodium niobate nano-particle/polymer composites with piezoelectric stability and their application to unsteady wind energy harvesters. J. Appl. Phys.
**2019**, 126, 224501. [Google Scholar] [CrossRef] - Hara, Y.; Yamamoto, Y.; Makihara, K. Self-sensing state estimation of switch-controlled energy harvesters. J. Intell. Mater. Syst. Struct.
**2020**, 31, 2326–2341. [Google Scholar] [CrossRef] - Khazaee, M.; Rezaniakolaie, A.; Rosendahl, L. A broadband macro-fiber-composite piezoelectric energy harvester for higher energy conversion from practical wideband vibrations. Nano Energy
**2020**, 76, 104978. [Google Scholar] [CrossRef] - Wang, Z.; Kurita, H.; Nagaoka, H.; Narita, F. Potassium sodium niobate lead-free piezoelectric nanocomposite generators based on carbon-fiber-reinforced polymer electrodes for energy-harvesting structures. Compos. Sci. Technol.
**2020**, 199, 108331. [Google Scholar] [CrossRef] - Wang, Y.; Yanaseko, T.; Kurita, H.; Sato, H.; Asanuma, H.; Narita, F. Electromechanical response and residual thermal stress of metal-core piezoelectric fiber/Al matrix composites. Sensors
**2020**, 20, 5799. [Google Scholar] [CrossRef] - Hara, Y.; Zhou, M.; Li, A.; Otsuka, K.; Makihara, K. Piezoelectric energy enhancement strategy for active fuzzy harvester with time-varying and intermittent switching. Smart Mater. Struct.
**2021**, 30, 015038. [Google Scholar] [CrossRef] - Atulasimha, J.; Flatau, A.B. A review of magnetostrictive iron–gallium alloys. Smart Mater. Struct.
**2011**, 20, 043001. [Google Scholar] [CrossRef] - Deng, Z.; Dapino, M.J. Review of magnetostrictive vibration energy harvesters. Smart Mater. Struct.
**2017**, 26, 103001. [Google Scholar] [CrossRef] - Nakajima, T.; Takeuchi, T.; Yuito, I.; Kato, K.; Saito, M.; Abe, K.; Sasaki, T.; Sekiguchi, T.; Yamaura, S. Effect of annealing on magnetostrictive properties of Fe–Co alloy thin films. Mater. Trans.
**2014**, 55, 556–560. [Google Scholar] [CrossRef] [Green Version] - Yamaura, S.; Nakajima, T.; Satoh, T.; Ebata, T.; Furuya, Y. Magnetostriction of heavily deformed Fe–Co binary alloys prepared by forging and cold rolling. Mater. Sci. Eng. B
**2015**, 193, 121–129. [Google Scholar] [CrossRef] [Green Version] - Liu, L.; Zhan, Q.; Yang, H.; Li, H.; Zhang, S.; Liu, Y.; Wang, B.; Tan, X.; Li, R.-W. Magnetostrictive GMR spin valves with composite FeGa/FeCo free layers. AIP Adv.
**2016**, 6, 035206. [Google Scholar] [CrossRef] - Bennett, S.P.; Baldwin, J.W.; Staruch, M.; Matis, B.R.; LaComb, J.; Jvan’tErve, O.M.; Bussmann, K.; Metzler, M.; Gottron, N.; Zappone, W.; et al. Magnetic field response of doubly clamped magnetoelectric microelectromechanical AlN-FeCo resonators. Appl. Phys. Lett.
**2017**, 111, 252903. [Google Scholar] [CrossRef] - Zhu, L.; Li, K.; Luo, Y.; Yu, D.; Wang, Z.; Wu, G.; Xie, J.; Tang, Z. Magnetostrictive properties and detection efficiency of TbDyFe/FeCo composite materials for nondestructive testing. J. Rare Earths
**2019**, 37, 166–170. [Google Scholar] [CrossRef] - Wang, W.; Jia, Y.; Xue, X.; Liang, Y.; Du, Z. Magnetostrictive effect in micro-dotted FeCo film coated surface acoustic wave devices. Smart Mater. Struct.
**2018**, 27, 105040. [Google Scholar] - Wang, Z.; Mori, K.; Nakajima, K.; Narita, F. Fabrication, modeling and characterization of magnetostrictive short fiber composites. Materials
**2020**, 13, 1494. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Bhatti, S.; Ma, C.; Liu, X.; Piramanayagam, S.N. Stress-induced domain wall motion in FeCo-based magnetic microwires for realization of energy harvesting. Adv. Electron. Mater.
**2019**, 5, 1800467. [Google Scholar] [CrossRef] [Green Version] - Seino, M.; Jiang, L.; Yang, Z.; Katabira, K.; Satake, T.; Narita, F.; Murasawa, G. Impact energy harvesting by Fe-Co fiber reinforced Al-Si matrix composite. Materialia
**2020**, 10, 100644. [Google Scholar] [CrossRef] - Yang, Z.; Wang, Z.; Seino, M.; Kumaoka, D.; Murasawa, G.; Narita, F. Twisting and reverse magnetic field effects on energy conversion of magnetostrictive wire metal matrix composites. Phys. Status Solidi RRL
**2020**, 14, 2000281. [Google Scholar] [CrossRef] - Yang, Z.; Wang, Z.; Nakajima, K.; Neyama, D.; Narita, F. Structural design and performance evaluation of FeCo/epoxy magnetostrictive composites. Compos. Sci. Technol.
**2021**, 210, 108840. [Google Scholar] [CrossRef] - Mori, K.; Horibe, T.; Maejima, K. Evaluation of the axial force in an FeCo bolt using the inverse magnetostrictive effect. Measurement
**2020**, 165, 108131. [Google Scholar] [CrossRef] - Ueno, T.; Yamada, S. Performance of energy harvester using iron–gallium alloy in free vibration. IEEE Trans. Magn.
**2011**, 47, 2407–2409. [Google Scholar] [CrossRef] - Mori, K.; Horibe, T.; Ishikawa, S.; Shindo, Y.; Narita, F. Characteristics of vibration energy harvesting using giant magnetostrictive cantilevers with resonant tuning. Smart Mater. Struct.
**2015**, 24, 125032. [Google Scholar] [CrossRef] - Xu, X.; Zhang, C.; Han, Q.; Chu, F. Hybrid energy harvesting from mechanical vibrations and magnetic field. Appl. Phys. Lett.
**2018**, 113, 013901. [Google Scholar] [CrossRef] - Yang, Z.; Nakajima, K.; Onodera, R.; Tayama, T.; Chiba, D.; Narita, F. Magnetostrictive clad steel plates for high-performance vibration energy harvesting. Appl. Phys. Lett.
**2018**, 112, 073902. [Google Scholar] [CrossRef] - Ghodsi, M.; Ziaiefar, H.; Mohammadzaheri, M.; Al-Yahmedi, A. Modeling and characterization of permendur cantilever beam for energy harvesting. Energy
**2019**, 176, 561–569. [Google Scholar] [CrossRef] - Patra, S. Design and development of magnetostrictive low power DC generator and vibration sensor. IEEE Sens. J.
**2020**, 20, 6324–6330. [Google Scholar] [CrossRef] - Liu, H.; Cong, C.; Cao, C.; Zhao, Q. Analysis of the key factors affecting the capability and optimization for magnetostrictive iron-gallium alloy ambient vibration harvesters. Sensors
**2020**, 20, 401. [Google Scholar] [CrossRef] [Green Version] - Saberkari, H.; Ghavifekr, H.B.; Shamsi, M. Comprehensive performance study of magneto cantilevers as a candidate model for biological sensors used in lab-on-a-chip applications. J. Med. Signals Sens.
**2015**, 5, 77–87. [Google Scholar] [CrossRef] - Guo, X.; Sang, S.; Guo, J.; Jian, A.; Duan, Q.; Ji, J.; Zhang, Q.; Zhang, W. A magnetoelastic biosensor based on E2 glycoprotein for wireless detection of classical swine fever virus E2 antibody. Sci. Rep.
**2017**, 7, 15626. [Google Scholar] [CrossRef] [Green Version] - Narita, F.; Wang, Z.; Kurita, H.; Li, Z.; Shi, Y.; Jia, Y.; Soutis, C. A review of piezoelectric and magnetostrictive biosensor materials for detection of COVID-19 and other viruses. Adv. Mater.
**2021**, 33, 2005448. [Google Scholar] [CrossRef] [PubMed] - Alshits, V.I.; Darinskii, A.N.; Lothe, J. On the existence of surface waves in half-infinite anisotropic elastic media with piezoelectric and piezomagnetic properties. Wave Motion
**1992**, 16, 265–283. [Google Scholar] [CrossRef] - Engdahl, G. Handbook of Giant Magnetostrictive Materia1-9ls; Academic: San Diego, CA, USA, 2000. [Google Scholar]
- Lee, J.; Boyd, J.G., IV; Lagoudas, D.C. Effective properties of three-phase electro-magneto-elastic composites. Int. J. Eng. Sci.
**2005**, 43, 790–825. [Google Scholar] [CrossRef] - Liang, C.; Morshed, S.; Prorok, B.C. Correction for longitudinal mode vibration in thin slender beams. Appl. Phys. Lett.
**2007**, 90, 221912. [Google Scholar] [CrossRef] - Grimes, C.A.; Ong, K.G.; Loiselle, K.; Stoyanov, P.G.; Kouzoudis, D.; Liu, Y.; Tong, C.; Tefiku, F. Magnetoelastic sensors for remote query environmental monitoring. Smart Mater. Struct.
**1999**, 8, 639–646. [Google Scholar] [CrossRef] - Yang, Z.; Onodera, R.; Tayama, T.; Watanabe, M.; Narita, F. Magnetomechanical design and power generation of magnetostrictive clad plate cantilever. Appl. Phys. Lett.
**2019**, 115, 243504. [Google Scholar] [CrossRef] - Liu, H.; Lim, C.W.; Gao, S.; Zhao, J. Effects analysis of bias and excitation conditions on power output of an environmental vibration energy harvesting device using Fe-Ga slice. Mechatronics
**2019**, 57, 20–28. [Google Scholar] [CrossRef] - Liu, H.; Li, W.; Sun, X.; Cong, C.; Cao, C.; Zhao, Q. Enhanced the capability of magnetostrictive ambient vibration harvester through structural configuration, pre-magnetization condition and elastic magnifier. J. Sound Vib.
**2021**, 492, 115805. [Google Scholar] [CrossRef] - Wang, Y.; Shi, Y.; Narita, F. Design and finite element simulation of metal-core piezoelectric fiber/epoxy matrix composites for virus detection. Sens. Actuators A Phys.
**2021**, 327, 112742. [Google Scholar] [CrossRef] - Narita, F.; Katabira, K. Stress-rate dependent output voltage for Fe
_{29}Co_{71}magnetostrictive fiber/polymer composites: Fabrication, experimental observation and theoretical prediction. Mater. Trans.**2017**, 58, 302–304. [Google Scholar] [CrossRef] [Green Version] - Guntupalli, R.; Hu, J.; Lakshmanan, R.S.; Huang, T.S.; Barbaree, J.M.; Chin, B.A. A magnetoelastic resonance biosensor immobilized with polyclonal antibody for the detection of Salmonella typhimurium. Biosens. Bioelectron.
**2007**, 22, 1474–1479. [Google Scholar] [CrossRef] [PubMed] - Zhang, K.; Zhang, L.; Fu, L.; Li, S.; Chen, H.; Cheng, Z.-Y. Magnetostrictive resonators as sensors and actuators. Sens. Actuators A
**2013**, 200, 2–10. [Google Scholar] [CrossRef] - Pandey, L.M. Design of engineered surfaces for prospective detection of SARS-CoV-2 using quartz crystal microbalance-based techniques. Expert Rev. Proteom.
**2020**, 17, 425–432. [Google Scholar] [CrossRef] [PubMed] - Pandey, L.M. Surface engineering of personal protective equipments (PPEs) to prevent the contagious infections of SARS-CoV-2. Surf. Eng.
**2020**, 36, 901–907. [Google Scholar] [CrossRef]

**Figure 1.**Finite element model of the Fe-Co/Ni clad plate. (

**a**) geometry and (

**b**) finite element mesh.

**Figure 5.**Calculated resonance frequency and frequency shift for various values of the distance between the weight and the clamped end.

**Figure 6.**Calculated resonance frequency and frequency shift for various values of the distance between the proof mass and the clamped end and the length of the mass.

**Figure 8.**Schematic of (

**a**) magnetostrictive harvester, (

**b**) voltage to frequency during detection, and (

**c**) bio-interfacial interaction of spike glycoprotein with mixed SAMs.

ij or kl | p or q |
---|---|

11 | 1 |

22 | 2 |

33 | 3 |

23 or 32 | 4 |

31 or 13 | 5 |

12 or 21 | 6 |

Material | Elastic Compliance * (×10 ^{−12} m^{2}/N) | Mass Density (kg/m ^{3}) | |||||
---|---|---|---|---|---|---|---|

${\mathit{s}}_{11}$ | ${\mathit{s}}_{33}$ | ${\mathit{s}}_{44}$ | ${\mathit{s}}_{66}$ | ${\mathit{s}}_{12}$ | ${\mathit{s}}_{13}$ | ||

Fe-Co | 5.5 | 5.5 | 14.3 | 14.3 | −1.65 | −1.65 | 8400 |

Ni | 5.0 | 5.0 | 13.1 | 13.1 | −1.55 | −1.55 | 8900 |

Material | Piezomagnetic Constant * (×10 ^{−12} m^{2}/A) | Magnetic Permittivity (×10^{−6} H/m) | |||
---|---|---|---|---|---|

${\mathit{d}}_{31}$ | ${\mathit{d}}_{33}$ | ${\mathit{d}}_{15}$ | μ_{11} | μ_{33} | |

Fe-Co | −60.3 | 125 | 318 | 1.26 | 1.26 |

Ni | 35.5 | −73.6 | −187.2 | 2.51 | 2.51 |

**Table 4.**Comparison of the output voltage densities of magnetostrictive cantilevers under bending vibration.

Material | Output Voltage Density (V/cm^{3}) | Bias Magnetic Field | Condition | Reference |
---|---|---|---|---|

Fe-Co/Ni clad plate | 2.1 | 0 mT | Frequency of 107 Hz | This work |

Fe-Co wire/epoxy Permendur plate | 15 0.0044 | 0 mT A permanent magnet | Frequency of 158 Hz Frequency of 64 Hz | [21] [27] |

Fe-Ga plate | 0.25 | 0 mT | Frequency of 75 Hz 5 g acceleration | [29] |

2.3 | 8 permanent magnets | Frequency of 75 Hz | [29] | |

Fe-Ga plate Fe-Ga/Cu laminate | 0.34 4.0 | 6.25 mT 8 permanent magnets | 2 g acceleration Frequency of 180 Hz Frequency of 25 Hz 1 g acceleration | [39] [40] |

Fe-Ga/piezoelectric laminate | 0.6 | 0.35 mT | Frequency of 105 Hz 0.1 g acceleration | [25] |

Traditional Piezoelectric | Traditional Magnetostrictive | Present Magnetostrictive | |
---|---|---|---|

Structure | Complicated | Simpler | Simpler |

Fabrication | Difficult | Easy | Easy |

Actuating | Electrical | Magnetic | Ambient vibration |

Sensing | Electrical | Magnetic | Magnetic |

Measured value | Frequency shift | Frequency shift | Output voltage |

Advantage | Compact configuration | Simple configuration | Simple configuration |

- | High flexibility | High flexibility | |

- | Wireless | Wireless | |

- | - | Rapid | |

Disadvantage/future work | Brittleness | Pick-up coil | Pick-up coil |

Charge leakage | Nonlinear effect | Need to improve sensitivity | |

Eddy current |

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**MDPI and ACS Style**

Mori, K.; Wang, Y.; Katabira, K.; Neyama, D.; Onodera, R.; Chiba, D.; Watanabe, M.; Narita, F.
On the Possibility of Developing Magnetostrictive Fe-Co/Ni Clad Plate with Both Vibration Energy Harvesting and Mass Sensing Elements. *Materials* **2021**, *14*, 4486.
https://doi.org/10.3390/ma14164486

**AMA Style**

Mori K, Wang Y, Katabira K, Neyama D, Onodera R, Chiba D, Watanabe M, Narita F.
On the Possibility of Developing Magnetostrictive Fe-Co/Ni Clad Plate with Both Vibration Energy Harvesting and Mass Sensing Elements. *Materials*. 2021; 14(16):4486.
https://doi.org/10.3390/ma14164486

**Chicago/Turabian Style**

Mori, Kotaro, Yinli Wang, Kenichi Katabira, Daiki Neyama, Ryuichi Onodera, Daiki Chiba, Masahito Watanabe, and Fumio Narita.
2021. "On the Possibility of Developing Magnetostrictive Fe-Co/Ni Clad Plate with Both Vibration Energy Harvesting and Mass Sensing Elements" *Materials* 14, no. 16: 4486.
https://doi.org/10.3390/ma14164486