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 引用本文: 赵翔, 袁铭泽, 方仕童, 李映辉. 基于自旋梁的压电振动能量采集与动力学分析. 力学学报, 2023, 55(10): 2228-2238.
Zhao Xiang, Yuan Mingze, Fang Shitong, Li Yinghui. Piezoelectric vibration energy harvesters and dynamic analysis based on the spinning beam. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(10): 2228-2238.
 Citation: Zhao Xiang, Yuan Mingze, Fang Shitong, Li Yinghui. Piezoelectric vibration energy harvesters and dynamic analysis based on the spinning beam. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(10): 2228-2238.

## PIEZOELECTRIC VIBRATION ENERGY HARVESTERS AND DYNAMIC ANALYSIS BASED ON THE SPINNING BEAM

• 摘要: 为研究轴向载荷及梁上外激励共同作用下自旋梁结构强迫振动的压电振动能量采集问题, 文章提出运用格林函数法求解自旋梁压电俘能器强迫振动下的电压解析解. 基于Euler-Bernoulli梁理论, 采用扩展Hamilton原理及PZT-5A压电本构, 建立了自旋梁压电俘能器强迫振动的力电耦合模型. 采用Laplace变换法求得耦合振动方程的格林函数解, 并根据线性叠加原理和格林函数的物理意义, 对耦合的系统方程进行解耦, 进而求得强迫振动下自旋梁压电俘能器的电压解析解. 数值计算中, 通过与现有文献中的解析解以及实验结果进行对比, 验证了本文解的有效性, 并分别分析了自旋梁压电俘能器的压电响应与电阻、转速等重要物理参数之间的关系. 数值分析研究表明: (1) 自旋梁俘能器的压电响应随电阻阻值的增大而增大, 直至阻值达到最优负载电阻; (2)通过调高转速, 可以提高压电俘能器的最大输出电压; (3)通过降低轴向载荷, 可在保持俘能器高效工作的情况下改善俘能器的高基频现象.

Abstract: In order to study the piezoelectric vibration energy harvesting problem of the forced vibration of a spinning beam structure under the combined effect of axial forces and external excitation on the beam, this paper proposes to use the Green's function method to solve the analytical solution of the voltage under the forced vibration of the spinning piezoelectric energy harvester. The extended Hamilton's principle and PZT-5A piezoelectric constitutive relationship are used to develop a force-electric coupling model for the spinning piezoelectric energy harvester of forced vibration based on the Euler-Bernoulli beam theory. Utilizing the Laplace transform, the explicit expressions of the Green's function of the coupled vibration equations can be acquired. Based on the linear superposition principle and the physical significance of the Green's function, the coupled system equations are decoupled to find the analytical solution of the voltage of the spinning piezoelectric energy harvester under forced vibration. In the numerical calculation, the validity of the solution of this paper is verified by comparing the present solution with the result of the existing literature as well as experimental result. The relationship between the piezoelectric response and physical parameters such as resistance and spinning speed of the energy harvester is analyzed separately. This research suggests that piezoelectric response of the spinning energy harvester increases with increasing resistance until the resistance reaches the optimal load resistance; the maximum output voltage of the energy harvester can be increased by turning up the spinning speed; by reducing the axial force, the high fundamental frequency of the energy harvester can be improved while maintaining the efficient operation of the energy harvester.

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