# A Hybrid Piezoelectric and Electromagnetic Broadband Harvester with Double Cantilever Beams

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## Abstract

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## 1. Introduction

_{33}piezoelectric mode, has a 65% higher power output than the stand-alone, single-harvesting mode devices [25]. Pyo et al. proposed a hybrid energy harvester with frequency up-conversion structures. The harvester comprises a flexible substrate and two (internal and external) cantilevers. The separate internal and external cantilevers for piezoelectric and electromagnetic transduction enable the piezoelectric internal cantilever to generate a high output power with large displacement vibration. The maximum output power of the hybrid harvester is 7.38 mW, with outputs of 1.35 and 6.03 mW for piezoelectric and electromagnetic conversion, respectively [26]. Foisal et al. designed and fabricated an array of four generators. In model A, four individual generators were placed side by side, whereas in model B the generators were placed one above the other. The experimental results showed that the power of model A and model B was 21.92 μW /cm

^{3}and 52.02 μW /cm

^{3}, respectively, at an acceleration of 0.5 g [27]. Ganapathy et al. designed and optimized a magnetically-tunable hybrid piezoelectric-triboelectric energy harvester (MT-HPTEH). Output power of 659 µW was obtained at 180 kΩ and 44 Hz from the optimized MT-HPTEH, with a theoretical-experimental discrepancy of less than 10%. The magnetic tunability enables the harvester to work at the desired frequency range from 38 Hz to 54 Hz with an open-circuit voltage ranging from 7.8 V to 20.314 V [28]. Zhu et al. designed and analyzed a magnetoelectric energy harvester that uses Terfenol-D/PZT/Terfenol-D laminate to harvest energy from nonlinear vibrations created by magnetic levitation. Due to the high energy density and strong magneto-mechanical coupling effect of the magnetostrictive material, the proposed harvester can generate very high voltage and power at low-frequency ranges [29]. Cao et al. researched the design and tested the output performance of a double-end clamped microelectromechanical system (MEMS)-coupled piezoelectric–electromagnetic energy harvester. The result showed that the capacity of this energy harvester was 12.23 times higher than that of a piezoelectric energy harvester (PEH) [30]. Low-frequency energy harvesters that harvest energy from human motion have been investigated. Rawnak et al. presented the WE-harvest system, a wearable energy harvesting system that combines piezoelectric and electromagnetic energy harvesters in one unit to generate electrical energy. Several power conditioning circuit topologies have been proposed for efficient energy extraction from the two sources. Experimental results have demonstrated that the combined topology enhances the power generation efficiency and enables stable DC output voltages [31]. Izadgoshasb et al. improved the efficiency of a PEH for obtaining energy from human motion using a double pendulum system coupled with magnetic interaction. Three PEH configurations were investigated: a conventional PEH with a cantilever beam (PEHCB), a PEH with a single pendulum system (PEHSP), and a PEH with a double pendulum system (PEHDP). The results demonstrated that the proposed PEHDP generated multiple impacts in each motion cycle and produced higher voltage and power than the conventional PEHCB [32]. Song et al. proposed a novel piezoelectric-electromagnetic hybrid vibration energy harvester (HVEH). As the magnets moved back and forth, the piezoelectric vibration-energy harvester (PVEH) generated stable output energy. A closed magnetic circuit was designed for an electromagnetic vibration energy harvester (EVEH) with a pair of magnets and a soft magnetic core. The experimental results showed that the optimal load resistance and the maximum output power of the PVEH were 398.7 kΩ and 87.9 μW, whereas that of the EVEH was 3.2 kΩ and 2.173 mW, respectively, in cycle experiments with a frequency of 5 Hz [33]. In addition, hybrid broadband vibration-energy harvesters have been developed and analyzed. He et al. investigated a low-frequency hybrid piezoelectric-electromagnetic-triboelectric broadband vibration-energy harvester. It consists of flexible piezoelectric-electromagnetic-triboelectric picking-up vibration structures to harvest broadband vibrations at low acceleration and at a wide vibration frequency. The piezoelectric, electromagnetic, and triboelectric EH units reach 3.5 Hz, 10.0 Hz, and 18.1 Hz operating bandwidth, respectively, under 0.5 g acceleration at 20 Hz [34]. The utilization of springs in energy harvesters has also been investigated. Aldawood et al. designed an improved magnetic spring-based energy harvester that uses a dual-mass spring and a nonlinear mechanical planar spring to improve the power metrics of traditional magnetic spring-based energy harvesters significantly. The improved harvester generates 1.97 mW/cm

^{3}g

^{2}at 0.4 g [35]. Febbo et al. developed a rotational power scavenging system as an alternative to cantilever beams attached to a hub. A versatile geometric configuration with two elastic beams and two heavy masses joined by a spring was proposed. The output power of a simple harvesting circuit, which served as an energy storage device, was in the range of 26–105 μW over the whole frequency range [36]. In addition, extensive research has recently been conducted on the static bending and free vibration responses of piezoelectric nanobeams, which is helpful in designing piezoelectric beam structures for practical applications. Doan et al. studied the mechanical behavior of the nanoplates under flexoelectric effects. This was the first study that examined the vibration response and static buckling of variable flexoelectric nanoplates using the finite element method (FEM) and novel shear deformation theory type hyperbolic sine functions [37]. Nguyen et al. combined the FEM with a novel third-order shear deformation beam theory (TSDT) to simulate the static bending and free vibration responses of rotating (around one fixed axis) piezoelectric nanobeams with geometrical imperfection, considering flexoelectric effects. The structures were placed on Pasternak’s elastic foundations. The results are highly applicable to the design of nanobeam structures in practice [38]. Phung et al. studied the rectangular plates subjected to static loads and supported on a discontinuous two-parameter elastic foundation. The formulae for the computations were developed from improved shear deformation theory. A parameter study was carried out to capture the effect of some material and geometrical parameters on the static response of structures [39]. Le et al. used the FEM to simulate the mechanical, electric, and polarization behaviors of piezoelectric nanoplates resting on elastic foundations subjected to static loads, considering the flexoelectric effect. The numerical results showed that the flexoelectric effect significantly affected the mechanical responses of the nanoplates [40].

## 2. HPEBH Structure and Mathematical Model

_{p}, and that of the elastic beam is 2c. The width of the piezoelectric patch is b, and the length of the piezoelectric cantilever beam is L

_{p}. The permanent magnet acts as the proof mass of the piezoelectric harvester, lowering the resonant frequency of the energy-harvesting structure. It also serves as the mover of the electromagnetic harvester. The motion of the permanent magnet generates an induced electromotive force in the fixed coil. The piezoelectric harvester and electromagnetic harvester are connected to the load resistances R

_{L1}and R

_{L2}, which match their internal resistance values.

_{1}represents the piezoelectric cantilever beam’s equivalent mass, and m

_{2}represents the magnet’s equivalent mass. $x\left(t\right)$ is the vibration exciter’s input vibration, $z\left(t\right)$ is the displacement of the piezoelectric cantilever beam’s equivalent mass, and $y\left(t\right)$ is the equivalent displacement of the magnet proof mass.

## 3. Finite Element Simulation

- A finite element simulation model of the HPEBH is established in COMSOL. The piezoelectric harvester is analyzed to obtain the resonant frequency, output voltage, optimum load resistance, and output power of the piezoelectric harvester.
- A model of an electromagnetic harvester is created in Maxwell software to analyze the harvester’s optimum load resistance and output power and obtain the electromagnetic motion’s damping force.
- The damping force obtained from the simulation of the electromagnetic harvester is used for the piezoelectric harvester to obtain its output voltage and output power in the hybrid simulation. The motion function of the end magnet is derived.
- Analysis of the electromagnetic harvester is conducted in Maxwell to obtain its output power in the hybrid simulation.

#### 3.1. Simulation of Piezoelectric Energy Harvesting

_{2}of the coil are 0.4 mm and 6 mm, respectively. The elastic coefficient is 0.5 $N/cm$ and the acceleration is 0.5 g.

#### 3.1.1. Harmonic Response Analysis of the Piezoelectric Harvester

#### 3.1.2. Impact of the Load Resistance on the Output Power of the Piezoelectric Harvester

#### 3.1.3. Impact of the Excitation Acceleration on the Output Power of the Piezoelectric Harvester

#### 3.1.4. Effect of the Ambient Frequency on the Amplitude of the Permanent Magnet

#### 3.2. Maxwell Simulation of the Electromagnetic Harvester

#### 3.2.1. Effect of Different Loads on the Power Output of the Electromagnetic Harvester

#### 3.2.2. Output Power of the Electromagnetic Harvester

#### 3.3. Energy-Harvesting Simulation of the HPEBH

## 4. Experimental Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**First-order vibration mode of the HPEBH: (

**a**) Displacement of the first resonance point; (

**b**) Displacement of the second resonance point.

**Figure 5.**The open-circuit voltage of the piezoelectric harvester with different masses of the permanent magnet.

**Figure 10.**Voltage (

**a**) and current (

**b**) of the electromagnetic harvester at the first resonance point.

**Figure 11.**Voltage (

**a**) and current (

**b**) of the electromagnetic harvester at the second resonance point.

**Figure 18.**Comparison of the output power of the HPEBH obtained from the simulation and the experiment.

Material | Parameters | Values |
---|---|---|

PZT-5H | Young’s modulus | 56 GPa |

Density | 7500 kg/m^{3} | |

Poisson’s ratio | 0.36 | |

Beryllium bronze | Young’s modulus | 112 GPa |

Density | 8780 kg/m^{3} | |

Poisson’s ratio | 0.35 | |

NdFeB | BH (max) | 35 MGOe |

Reference | Frequency (Hz) | Acceleration (g) | Power (mW) | Power Density (μW/cm^{3}) |
---|---|---|---|---|

This work | 10.1 | 0.5 | 7.19 | 44.65 |

Lin et al. [23] | 25 | 1.0 | 2.173 | 85.28 * |

Li et al. [24] | 5.57873 | 1.0 | 5.49 | 27.56 |

Challa et al. [25] | 21.6 | 0.332 | 9.5 | |

Pyo et al. [26] | 57 | 7.38 | 2.952 | |

Foisal et al. [27] | 8.5 | 0.5 | 2.09 | 52.02 |

Ganapathy et al. [28] | 44 | 0.659 | 10.98 | |

Song et al. [33] | 5 | 2.2609 | 11.3 | |

He et al. [34] | 20 | 0.5 | 0.1075 | 0.676 |

Aldawood et al. [35] | 11 | 0.4 | 68.78 | 315.2 |

^{2}from the data provided in the article.

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**MDPI and ACS Style**

Jiang, B.; Zhu, F.; Yang, Y.; Zhu, J.; Yang, Y.; Yuan, M.
A Hybrid Piezoelectric and Electromagnetic Broadband Harvester with Double Cantilever Beams. *Micromachines* **2023**, *14*, 240.
https://doi.org/10.3390/mi14020240

**AMA Style**

Jiang B, Zhu F, Yang Y, Zhu J, Yang Y, Yuan M.
A Hybrid Piezoelectric and Electromagnetic Broadband Harvester with Double Cantilever Beams. *Micromachines*. 2023; 14(2):240.
https://doi.org/10.3390/mi14020240

**Chicago/Turabian Style**

Jiang, Bing, Fan Zhu, Yi Yang, Jingyu Zhu, Yuting Yang, and Ming Yuan.
2023. "A Hybrid Piezoelectric and Electromagnetic Broadband Harvester with Double Cantilever Beams" *Micromachines* 14, no. 2: 240.
https://doi.org/10.3390/mi14020240