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Nonlinear analysis of functionally graded piezoelectric energy harvesters

机译：功能梯度压电能量收集器的非线性分析

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摘要

This study deals with nonlinear vibrational analysis of functionally graded piezoelectric energy harvesters (FGPEH) carrying concentrated mass at free end, while taking into account the geometrical nonlinear terms as well as electromechanical couplings. Hamilton's principle and Rayleigh's beam theory are utilized to obtain the coupled electromechanical governing equations. The first mode shape of the system is derived analytically which is also validated by comparing it with numerical findings of a three-dimensional finite element simulation performed in COMSOL Multiphysics commercial software. The Galerkin projection method is employed along with a single mode approximation to derive the nonlinear coupled electromechanical governing equations which are then solved analytically using the method of multiple time scales perturbation technique for both cases of free and forced vibrations. Time domain responses of free vibration are compared with those of numerical simulations carried out in MATLAB and excellent agreement is observed. Moreover, the nonlinear frequency responses of the forced vibration are obtained for the case of near resonance excitation. A parametric study is also accomplished to reveal the effects of power low index of the FG material as well as the scaled amplitude of the input displacements of the base on the shape of the frequency response.
机译：这项研究涉及功能梯度压电能量收集器（FGPEH）的非线性振动分析，该能量收集器在自由端承载集中质量，同时考虑了几何非线性项以及机电耦合。利用汉密尔顿原理和瑞利梁理论来获得耦合的机电控制方程。通过分析得出系统的第一模式形状，并将其与在COMSOL Multiphysics商业软件中进行的三维有限元模拟的数值结果进行比较，从而对其进行验证。将Galerkin投影法与单模近似一起使用，以导出非线性耦合机电控制方程，然后针对自由振动和强制振动两种情况，使用多时标摄动技术对这些方程进行解析求解。将自由振动的时域响应与在MATLAB中进行的数值模拟进行了比较，并观察到了极好的一致性。此外，对于近共振激励的情况，获得了强迫振动的非线性频率响应。还完成了一项参数研究，以揭示FG材料的低功率指数的影响以及基于频率响应形状的底座输入位移的缩放​​幅度。

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