# Development of Piezoelectric Harvesters with Integrated Trimming Devices

^{*}

## Abstract

**:**

## Featured Application

**Trimming devices integrated with the structural layer of the harvester are proposed for improving energy harvesting at low frequency and in the presence of periodic excitation with multiple harmonics.**

## Abstract

## 1. Introduction

## 2. Preliminary Design of Prototypes

^{3}); this solution allowed to obtain a structure with low damping. The mass elements were small brass discs, whose masses were measured by means of a balance having a resolution of 0.1 mg.

## 3. Analytical Model of Prototypes

## 4. Experimental Tests and Results

^{−2}, harvester PPA 1001 generates in resonance 1.61 mW, whereas harvester PPA 1001 with A1 generates 0.97 mW at the first resonance and 0.37 mW at the second resonance.

## 5. Numerical Model and Validation

^{−2}and takes place at 125.6 Hz, the experimental values being 1.85 V/ms

^{−2}at 126.4 Hz. With optimal load resistance (12.7 kΩ) the numerical resonance peak is 0.60 V/ms

^{−2}and takes place at 124.5 Hz, the experimental values being 0.64 V/ms

^{−2}at 125.6 Hz.

## 6. Numerical Simulation of Harvesters with ITDs

#### 6.1. Open Circuit Voltage

^{−2}), a bit smaller than the PPA 1001 alone. The second resonance peak, which appears at 154.0 Hz, is much lower than the main peak and is caused by the excitation of the second mode of vibration generated by ITD1. For comparison, Figure 13a shows the effect of a large tip mass (0.59 g). In this case the trimming frequency is 88.1 Hz and the peak value is 2.7 V/ms

^{−2}.

^{−2}and 0.57 V/ms

^{−2}respectively.

#### 6.2. Generated Power

^{−2}was simulated. Calculated results are represented in Figure 16, and the powers generated by the harvesters with ITDs are compared with the powers generated by the harvester alone and by the harvester with a tip mass that trims the harvester to the same frequency.

#### 6.3. Stress Analysis

^{−2}at the main resonance frequency, which coincides with the low frequency peak of the harvesters with ITDs and with the main peak of the others.

_{x}was calculated, since it is the most important stress component caused by harvester bending. Stress σ

_{x}was evaluated along the centerline of the upper surface of the PZT layer, which is at the largest distance from the neutral axis of the composite cross-section. The trace of this line is point P of Figure 9.

## 7. Discussion

## 8. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 3.**Open circuit FRFs (frequency response functions) of the prototypes calculated by means of the analytical model.

**Figure 4.**Phases of the displacements of the harvester and of the DVA calculated by means of the analytical model.

**Figure 5.**Open circuit FRFs of the prototypes calculated by means of the analytical model. Effect of trimming frequency.

**Figure 6.**FRFs of the prototypes with optimal resistance calculated by means of the analytical model.

**Figure 8.**Measured FRFs of the harvester alone, with tip mass and with cantilever DVA. (

**a**) Open circuit. (

**b**) Optimal load resistance.

**Figure 10.**Validation of the numerical model, FRFs of PPA 1001 in open circuit and with optimal load resistance.

**Figure 11.**Validation of the numerical model, FRFs of PPA 1001 with A1 in open circuit and with optimal load resistance.

**Figure 13.**Numerical results, FRFs of the harvester with ITDs (integrated trimming devices), with tip mass and alone; open circuit condition. (

**a**) ITD1, (

**b**) ITD2.

**Figure 14.**Numerical results, strains in the piezo layer of the harvester with ITD1. (

**a**) Modal shape at the first resonance (89.8 Hz). (

**b**) Strain modulus at the first resonance (89.9 Hz). (

**c**) Strain phase at the first resonance (89.8 Hz). (

**d**) Modal shape at the second resonance (154.0 Hz). (

**e**) Strain modulus at the second resonance (154.0 Hz). (

**f**) Strain phase at the second resonance (154.0 Hz).

**Figure 15.**Numerical results, strains in the piezo layer of the harvester with ITD2. (

**a**) Modal shape at the first resonance (89.7 Hz). (

**b**) Strain modulus at the first resonance (89.7 Hz). (

**c**) Strain phase at the first resonance (89.7 Hz). (

**d**) Modal shape at the second resonance (179.5 Hz). (

**e**) Strain modulus at the second resonance (179.5 Hz). (

**f**) Strain phase at the second resonance (179.5 Hz).

**Figure 16.**Numerical results, power generated by PPA 1001 equipped with trimming devices, optimal load resistance, base acceleration 10 ms

^{−2}(1 g). (

**a**) ITD1, (

**b**) ITD2.

**Table 1.**Analytical results: resonance frequencies and corresponding amplitudes of the prototypes in open circuit condition.

Harvester | 1st Mode | 2nd Mode | $\Delta $F (Hz) | ||
---|---|---|---|---|---|

Frequency ${\mathit{f}}_{1}$ (Hz) | Peak Amplitude (V/ms^{−2}) | Frequency ${\mathit{f}}_{2}$ (Hz) | Peak Amplitude (V/ ms^{−2}) | ||

PPA 1001 | 125.5 | 1.69 | - | - | - |

PPA 1001 + A1 | 97.1 | 1.57 | 161.5 | 0.39 | 64.4 |

PPA 1001 + A2 | 102.8 | 1.34 | 152.6 | 0.46 | 49.8 |

PPA 1001 + A3 | 107.7 | 1.18 | 145.6 | 0.52 | 37.9 |

**Table 2.**Resonance frequencies of the coupled systems and corresponding amplitudes of the prototypes. Mean values of five tests.

Harvester | 1st Mode | 2nd Mode | $\Delta $F (Hz) | ||||
---|---|---|---|---|---|---|---|

Frequency ${\mathit{f}}_{1}$ (Hz) | Peak Amplitude (V/ms^{−2}) | Damping Ratio $\mathit{\zeta}$ | Frequency ${\mathit{f}}_{2}$ (Hz) | Peak Amplitude (V/ms^{−2}) | Damping Ratio $\mathit{\zeta}$ | ||

PPA 1001 | 126.4 | 1.85 | 0.0072 | - | - | - | - |

PPA 1001 + Tip Mass | 90.0 | 2.48 | 0.0087 | - | - | - | - |

PPA 1001 + A1 | 88.2 | 1.35 | 0.0087 | 158.9 | 0.55 | 0.0085 | 70.7 |

PPA 1001 + A2 | 93.2 | 1.33 | 0.0080 | 156.4 | 0.61 | 0.0077 | 63.2 |

PPA 1001 + A3 | 97.4 | 1.25 | 0.0073 | 148.3 | 0.79 | 0.0071 | 50.9 |

**Table 3.**Dimensional characteristics of the zirconate/lead titanate (PZT) layer, generated power ad maximum stress of PPA 1001 and various harvesters trimmed to the same frequency, base acceleration is 10 ms

^{−2}.

Harvester | L (mm) | be (mm) | bc (mm) | Frequency (Hz) | Peak Power (mW) | $\mathit{\sigma}$ (MPa) |
---|---|---|---|---|---|---|

PPA 1001 | 40.1 | 20.8 | 20.8 | 124.5 | 1.42 | 55 |

PPA + ITD1 | 40.1 | 20.8 | 20.8 | 89.3 | 1.10 | 37 |

PPA + ITD2 | 40.1 | 20.8 | 20.8 | 89.5 | 0.95 | 33 |

PPA + tip mass | 40.1 | 20.8 | 20.8 | 87.3 | 2.33 | 85 |

Slender-rectangular | 48.8 | 17.5 | 17.5 | 87.6 | 1.95 | 70 |

Inverse tapered | 41.1 | 31.6 | 10.0 | 87.4 | 2.30 | 118 |

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**MDPI and ACS Style**

Doria, A.; Medè, C.; Fanti, G.; Desideri, D.; Maschio, A.; Moro, F. Development of Piezoelectric Harvesters with Integrated Trimming Devices. *Appl. Sci.* **2018**, *8*, 557.
https://doi.org/10.3390/app8040557

**AMA Style**

Doria A, Medè C, Fanti G, Desideri D, Maschio A, Moro F. Development of Piezoelectric Harvesters with Integrated Trimming Devices. *Applied Sciences*. 2018; 8(4):557.
https://doi.org/10.3390/app8040557

**Chicago/Turabian Style**

Doria, Alberto, Cristian Medè, Giulio Fanti, Daniele Desideri, Alvise Maschio, and Federico Moro. 2018. "Development of Piezoelectric Harvesters with Integrated Trimming Devices" *Applied Sciences* 8, no. 4: 557.
https://doi.org/10.3390/app8040557