# A Pavement Piezoelectric Energy Harvester for Small Input Displacements

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Design Concept and Modeling

_{31}mode [24]. Based on the working principle of PZT, the mechanical stress in the PZT plate is selected as the indicator to analyze the mechanical response of ADBs, determine the configuration of each component and evaluate the electromechanical conversion performance of the energy harvester [25,26].

#### 2.1. Design Concept

#### 2.2. Modeling

_{1}and s

_{2}, and q distributes in the first s

_{2}/3 from C. Then, the reaction force R

_{A}can be calculated as

_{p}= qs

_{2}/3 is the equivalent concentrated force of q. Then, the deflection curve equation of the overhanging beam is represented as

_{c}is

_{2}). Meanwhile, this adjustment also influences the force R

_{A}and may decrease the harvesting efficiency. Therefore, a more practical method is to improve the stiffness of the seesaw (e.g., promoting the elasticity modulus of the used material and optimizing the dimension). Under this circumstance, the reaction force R

_{A}will trigger the ADBs to generate electric energy when a step is loaded onto the input end of the seesaw.

_{A}is the total force acting on all beams, which each ADB withstands as tensile or pressure force. Herein, a stretched ADB below the seesaw is modeled when the force is loaded. Under the force transmitted from seesaw F

_{A}(F

_{A}= R

_{A}/N, N is the number of used ADBs), a deformation u

_{1}and corresponding stress σ

_{A}appears in ADB, which can be expressed as

_{A}is Young’s modulus of the ADB material, and l, b, and t are the length, width, and thickness of ADB, respectively. Under the similar displacement u

_{1}at its free end, the conventional bending cantilever beam (BCB) will produce a linearly distributed stress along its length direction, and the maximum amplitude appears at the fixed end of the cantilever as

^{®}14.5. All DOFs of their fixed end are constrained, and the same displacement of 0.5 mm is loaded onto their free ends. The displacement in ADB is along the length direction, and the force in BCB is perpendicular to the cantilever surface. The material parameters originate from brass and are included in Table 1. Figure 3 shows the simulated stress distribution on the top surface of each beam. Generally, the stress of ADB features a uniform distribution on most of the surface, except for the locally sharp changes near fixing or loading boundaries. On the contrary, the stress in BCB emerges an obvious decrease as the viewpoint is away from the fixed end.

## 3. Prototype and Experiments

#### 3.1. Comparison of Single ADB and BCB

#### 3.2. Characterizations and Applications of Proposed PPEH

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The schematic diagram for the proposed PPEH: (

**a**) a single ADB with a PZT plate; (

**b**) exploded view of an ADB; (

**c**) the structural mode of proposed PPEH; (

**d**) the structural mode of seesaw and ADBs; (

**e**) the loading ways for conventional beams (

**up**and

**middle**) and ADB (

**below**).

**Figure 4.**The experimental fixture for validating ADB and BCB approaches” (

**a**) scheme for ADB, (

**b**) scheme for BCB, and (

**c**) the photo of the fabricated fixture.

**Figure 6.**(

**a**) the measured open-circuit voltage of ADB and BCB and (

**b**) the residuals of linear fits.

**Figure 9.**The output capacity of the proposed PPEH: (

**a**) optimal load and corresponding output power; (

**b**) the charged voltage over a 2200-μF capacitor.

**Figure 10.**The slops of linearly fitting lines for the voltage-displacement curves after sustaining different numbers of cyclic loads.

**Figure 11.**Applying proposed PPEH in powering a low-power sensing device. (

**a**) Circuit diagram of the system; (

**b**) Picture of the powered sensing device.

Material Parameters | Beam Dimensions | ||||
---|---|---|---|---|---|

Young’s Modulus (GPa) | Poisson’s Ratio | Density (kg/m ^{3}) | Length (mm) | Width (mm) | Thickness (mm) |

91 | 0.36 | 8600 | 50 | 11 | 0.2 |

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## Share and Cite

**MDPI and ACS Style**

Yin, B.; Wei, J.; Jiang, X.; Liu, Y.
A Pavement Piezoelectric Energy Harvester for Small Input Displacements. *Micromachines* **2023**, *14*, 292.
https://doi.org/10.3390/mi14020292

**AMA Style**

Yin B, Wei J, Jiang X, Liu Y.
A Pavement Piezoelectric Energy Harvester for Small Input Displacements. *Micromachines*. 2023; 14(2):292.
https://doi.org/10.3390/mi14020292

**Chicago/Turabian Style**

Yin, Bin, Jiaming Wei, Xin Jiang, and Yan Liu.
2023. "A Pavement Piezoelectric Energy Harvester for Small Input Displacements" *Micromachines* 14, no. 2: 292.
https://doi.org/10.3390/mi14020292