端部质量块对悬臂梁型挠曲电俘能器性能的影响

Effects of tip mass on performance of cantilever beam flexoelectric energy harvesters

端部质量块对悬臂梁型挠曲电俘能器的性能具有显著的影响.以电吉布斯自由能为基础,基于Euler-Bernoulli梁模型,利用挠曲电材料的变分方法,推导带端部质量块的挠曲电俘能器结构的机电耦合动力学控制方程和相应的力电边界条件;利用分离变量法推导结构在短路条件下的振型正交条件和归一化振型参数;结合模态叠加法推导出挠曲电俘能器在外加简谐激励条件下位移和电势响应的解析形式.数值分析结果表明,端部质量块质量的增加和尺寸的减小可以提高俘能器输出功率并降低其共振频率,并且具有调节挠曲电俘能器最优外加电阻负载的功能.此外,当端部质量块尺寸一定时,端部质量块的质量越大,采用质点模型分析所带来的误差越明显.

The tip mass has a significant influence on the performance of flexoelectric energy harvesters.In this paper,based on Euler-Bernoulli beam assumption and the electric Gibbs free energy,the dynamic electromechanical coupled governing equations and the corresponding boundary conditions of flexoelectric energy harvesters are derived using the variational principle method.The modal orthometric conditions and parameters for the normalized mode of vibration are obtained by the separation of variable method.Furthermore,the mode superposition method is used to derive the analytical expressions of the displacement and electric potential responses of the flexoelectric energy harvester with the extrinsic harmonic mechanical excitation. Numerical results indicate that the increase of the value of mass and decrease of the size of the tip mass not only can increase the output power density and decrease the resonant frequency of the energy harvester,but also can adjust the optimal resistance.In addition,when the size of mass is fixed,the value of mass of the tip mass is larger,and the error caused by considering the tip mass as a particle becomes more distinct.