参数和直接激励下附加端部质量块悬臂梁压电俘能器的多尺度法非线性分析

夏光辉,王建国

振动与冲击 ›› 2020, Vol. 39 ›› Issue (19) : 69-77.

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PDF(1692 KB)
振动与冲击 ›› 2020, Vol. 39 ›› Issue (19) : 69-77.
论文

参数和直接激励下附加端部质量块悬臂梁压电俘能器的多尺度法非线性分析

  • 夏光辉,王建国
作者信息 +

Nonlinear dynamic analysis for a cantilever beam with a tip mass piezoelectric harvester under parametric and direct excitations with multi-scale method

  • XIA Guanghui, WANG Jianguo
Author information +
文章历史 +

摘要

考虑几何非线性、阻尼非线性和梁的轴向不可伸长条件,本文通过Hamilton变分原理,建立了一个附加端部质量块悬臂梁压电俘能器在受到参数和直接激励下的非线性机电耦合的运动微分方程。压电俘能器为压电双晶片悬臂梁结构。利用Galerkin法,非线性机电耦合的偏微分方程被降阶为非线性机电耦合型Mathieu-Duffing方程。为了研究俘能器在其主要的一阶共振情况下的响应,采用了多尺度法获得了梁的位移、输出电压和输出功率的解析表达式。利用解析表达式研究了参数激励和直接激励共同作用下阻抗,阻尼系数和端部质量块等对压电俘能器性能的影响。

Abstract

Here, considering geometric nonlinearity, damping nonlinearity and axial inextensibility of beams, the electro-mechanical coupled nonlinear dynamic equation of a cantilever beam with a tip mass piezoelectric energy harvester under parametric and direct excitations was established by using Hamilton variational principle. In fact, the piezoelectric energy harvester is a piezoelectric bimorph cantilever beam structure. Using Galerkin method, the electro-mechanical coupled nonlinear dynamic equation was reduced to an electro-mechanical coupled nonlinear Mathieu-Duffing equation. In order to study the first-order resonance response of the energy harvester, the multi-scale method was used to obtain the analytical expressions for beam deflection, output voltage and output power of the energy harvester. These analytical expressions were used to study influences of impedance, damping coefficient and tip mass under parametric and direct excitations on performances of the piezoelectric energy harvester.

关键词

参数激励 / 直接激励 / 端部质量块 / 压电俘能 / 几何非线性 / 阻尼非线性 / 多尺度法

Key words

parametric excitation / direct excitation / tip mass / piezoelectric energy harvesting / geometric nonlinearity / damping nonlinearity / multi-scale method

引用本文

导出引用
夏光辉,王建国. 参数和直接激励下附加端部质量块悬臂梁压电俘能器的多尺度法非线性分析[J]. 振动与冲击, 2020, 39(19): 69-77
XIA Guanghui, WANG Jianguo. Nonlinear dynamic analysis for a cantilever beam with a tip mass piezoelectric harvester under parametric and direct excitations with multi-scale method[J]. Journal of Vibration and Shock, 2020, 39(19): 69-77

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