双向激励下非线性压电俘能系统的稳态响应分析

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (23) : 102-108.

论文

夏光辉1,2,3,康小方1,2,3,李聪1,陈雷雨2,3,许庆虎1,2,3,满大伟1,2,3

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Steady state response analysis of nonlinear piezoelectric energy capture system under bidirectional excitations

XIA Guanghui1,2,3, KANG Xiaofang1,2,3, LI Cong1, CHEN Leiyu2,3, XU Qinghu1,2,3, MAN Dawei1,2,3

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摘要

基于基础激励的多向性和实际环境中的低频率环境，研究了在固定基础端受到水平和垂直双向激励的附加端部质量块悬臂梁压电俘能系统的非线性稳态响应问题。通过Hamilton原理对一个附加端部质量块悬臂梁双晶片压电俘能系统模型的非线性偏微分方程进行理论推导和计算分析。假设此悬臂梁为轴向不可伸长的Euler-Bernoulli梁，此模型主要包含几何非线性和阻尼非线性。利用Galerkin法将非线性偏微分方程降阶得到双向激励作用下附加端部质量块悬臂式压电俘能系统的机电耦合运动微分方程。采用多尺度法研究压电俘能系统在其主要的一阶共振情况下的响应，获得了俘能系统的垂直位移、输出电压和输出功率的解析表达式。得到其主要一阶垂直位移幅值，输出电压幅值和输出功率幅值。分析了不同激励情况下，激励相位等对压电俘能系统俘能性能的影响。
关键词：双向激励；非线性；压电俘能；多尺度法；相位

Abstract

Based on the multi-directionality of the foundation excitation and the low frequency environment in the real environment, the nonlinear steady-state response of the piezoelectric energy harvesting system with an additional end mass cantilever beam subjected to horizontal and vertical two-direction excitations at the fixed base end is studied. Based on Hamilton principle, the nonlinear partial differential equation of a cantilever bimorph piezoelectric energy harvesting system with an additional end mass is derived and analyzed. It is assumed that the cantilever is an axially non elongated Euler Bernoulli beam, and the model mainly includes geometric nonlinearity and damping nonlinearity. By using Galerkin method, the nonlinear partial differential equation is reduced to obtain the electromechanical coupling motion differential equation of cantilever piezoelectric energy harvesting system with end mass under two-direction excitations. The response of piezoelectric energy harvesting system under the main first-order resonance is studied by using the method of multiple scales. The analytical expressions of vertical displacement, output voltage and output power are obtained. The main first-order vertical displacement amplitude, output voltage amplitude and output power amplitude are obtained. The influence of excitation phase on the energy harvesting performance of piezoelectric energy harvesting system under different excitation conditions is analyzed.
Key words: bidirectional excitations; nonlinearity; piezoelectric energy harvesting; method of multiple scales; phase

导出引用

夏光辉1,2,3,康小方1,2,3,李聪1,陈雷雨2,3,许庆虎1,2,3,满大伟1,2,3. 双向激励下非线性压电俘能系统的稳态响应分析[J]. 振动与冲击, 2022, 41(23): 102-108

XIA Guanghui1,2,3, KANG Xiaofang1,2,3, LI Cong1, CHEN Leiyu2,3, XU Qinghu1,2,3, MAN Dawei1,2,3. Steady state response analysis of nonlinear piezoelectric energy capture system under bidirectional excitations[J]. Journal of Vibration and Shock, 2022, 41(23): 102-108

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