# Multimodal Multidirectional Piezoelectric Vibration Energy Harvester by U-Shaped Structure with Cross-Connected Beams

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Design and Simulation

#### 2.1. Design and Working Principle

#### 2.2. Analysis for Proof-of-Concept

^{3}and 0.38 for brass, 60 GPa, 7750 kg/m

^{3}, and 0.36 for PZT-5A.

^{2}) acceleration to the proposed model. Figure 2a shows the distribution of equivalent stress under x-axis acceleration, in which the corresponding stress mainly concentrates in the lower beam of vertical leg; the y-axis acceleration can produce a stress concentration near the fixed end of upper beam, as shown in Figure 2b. Then, the maximum stress under a z-axis acceleration symmetrically distributes near both sides of proof mass. Thus, these three stress concentrated regions are chosen to paste piezoelectric ceramics to maximize the sensed mechanical energy.

_{i}, M

_{i}are the equivalent stiffness and mass of whole structure.

_{iu}is determined by the bending of two upper beams and M

_{iu}is dominated by the mass distribution of lower parts, including proof mass, lower beams, and horizontal beam. Thus,

_{t}is mass of proof mass. EI is the flexural rigidity of upper beam, which can be obtained by analyzing the feature of piezoelectric cantilever.

_{1}and EI

_{2}are the flexural rigidity of lower and horizontal beams, respectively. l

_{1}and l

_{2}are their lengths. M

_{1}and M

_{2}are mass of lower and horizontal beams. α

_{i}and β

_{i}are the coefficients determined by structural configuration. More information can be found in [33].

## 3. Prototype and Experimental Setup

## 4. Results and Discussions

#### 4.1. Experimental Results

#### 4.2. Discussions

^{3}g

^{2}Hz), which is close to many 1D PVEHs. Therefore, the proposed PVEH using improved U-shaped structural as a multidimension, multimodal energy harvesting architecture shows potential for practical applications in the daily environment.

#### 4.3. Applications

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**The stress distribution in the proposed U-shaped structure when stimulated by (

**a**) x-axis, (

**b**) y-axis, and (

**c**) z-axis accelerations.

**Figure 4.**The deformations from harmonic response analysis when the U-shaped structure excited by (

**a**) x-axis, (

**b**) y-axis, and (

**c**) z-axis accelerations.

**Figure 9.**Output voltage of different beams versus α at the first three resonant frequencies: (

**a**) upper beam, (

**b**) horizontal beam, and (

**c**) lower beam.

**Figure 11.**Output voltage of different beams versus β at the first three resonant frequencies: (

**a**) upper beam, (

**b**) horizontal beam, and (

**c**) lower beam.

**Figure 12.**Output power versus loaded resistance under the maximum voltage for (

**a**) upper beam, (

**b**) lower beam and (

**c**) horizontal beam.

**Figure 13.**Applying proposed PVEH in harvesting sustained vibration. (

**a**) Output voltage of proposed PVEH; (

**b**) The voltage over charged capacitor.

**Figure 14.**Applying proposed PVEH in harvesting stamping vibration. (

**a**) Output voltage of proposed PVEH; (

**b**) The voltage over charged capacitor.

**Figure 15.**Applying proposed PVEH in powering a wireless sensor node. (

**a**) Circuit diagram of the wireless sensor node device; (

**b**) Picture of signal transmission through Bluetooth.

Components | Valid Length | Width | Thickness |
---|---|---|---|

PZT-5A | 12 | 8 | 0.2 |

Horizontal beam | 100 | 10 | 0.2 |

Lower beam | 50 | 10 | 0.2 |

Upper beam | 40 | 10 | 0.2 |

Orders | Measured | Simulated | Deviation |
---|---|---|---|

1st | 2.6 | 2.26 | 0.34 |

2nd | 9.1 | 10.79 | 1.69 |

3rd | 11.4 | 13.89 | 2.35 |

Works | Excitations (1D/2D/3D) | Acc. (g) | Fre. (Hz) | Power (µW) | Volu. (mm^{3}) | NVPD (µW/(mm^{3}g^{2}Hz)) |
---|---|---|---|---|---|---|

[34] | 1D | 0.041 | 27.5 | 93 | 6300 | 0.3139 |

[35] | 1D | 1 | 160 | 2490 | 880 | 0.0177 |

[23] | 1D | 0.1 | 12 | 442 | 8400 | 0.4383 |

[36] | 2D | 3 | 18 | 963.9 | 3120 | 0.00191 |

[32] | 3D | 0.5 | 23.7 | 9.2 | 4256 | 0.00036 |

[30] | 3D | 0.008 | 4.56 | - | 982 | - |

[28] | 3D | 0.5 | 8 | 110.3 | 3480 | 0.0158 |

[31] | 3D | 1 | 2.9 | 306 | 4507 | 0.0234 |

This work | 3D | 0.5 | 2.5 | 314 | 4586 | 0.1115 |

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**MDPI and ACS Style**

Qin, H.; Mo, S.; Jiang, X.; Shang, S.; Wang, P.; Liu, Y.
Multimodal Multidirectional Piezoelectric Vibration Energy Harvester by U-Shaped Structure with Cross-Connected Beams. *Micromachines* **2022**, *13*, 396.
https://doi.org/10.3390/mi13030396

**AMA Style**

Qin H, Mo S, Jiang X, Shang S, Wang P, Liu Y.
Multimodal Multidirectional Piezoelectric Vibration Energy Harvester by U-Shaped Structure with Cross-Connected Beams. *Micromachines*. 2022; 13(3):396.
https://doi.org/10.3390/mi13030396

**Chicago/Turabian Style**

Qin, Hongbo, Shuting Mo, Xin Jiang, Siyao Shang, Peng Wang, and Yan Liu.
2022. "Multimodal Multidirectional Piezoelectric Vibration Energy Harvester by U-Shaped Structure with Cross-Connected Beams" *Micromachines* 13, no. 3: 396.
https://doi.org/10.3390/mi13030396