考虑材料非线性时压电发电悬臂梁的主共振响应分析

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振动与冲击 ›› 2014, Vol. 33 ›› Issue (19) : 8-16.

论文

考虑材料非线性时压电发电悬臂梁的主共振响应分析

郭抗抗 1，2 ，曹树谦 1，2

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Primary Resonance of Piezoelectric Energy Harvesters Considering Nonlinearities of Piezoelectric Material

GUO Kang-kang 1,2 CAO Shu-qian 1,2

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文章历史 +

摘要

针对单晶压电悬臂梁发电系统进行了动力学建模及主共振响应分析。首先在考虑压电材料非线性的情况下，利用广义Hamilton原理、Rayleigh-Ritz法、Euler-Bernoulli梁理论等建立了单晶压电悬臂梁发电结构的机电耦合模型；其次利用多尺度法对系统进行了主共振二次近似响应分析，得到了谐振频率附近解的特性与系统参数的关系，揭示了压电材料非线性、外激励参数及负载电阻对系统响应的影响规律；最后通过数值计算验证了解析解的正确性。结论表明，压电材料的非线性特性会导致近似解的共振峰向左偏移，呈现软特性的非线性特征；当激励频率变化时，系统响应存在多解、跳跃等现象，多解区有2个稳定焦点和1个不稳定鞍点；主共振解的真正实现取决于系统的稳定性条件及初始条件的选取；系统存在最佳匹配负载电阻范围，对应系统的发电功率较大。

Abstract

Dynamic modeling and primary response analysis of piezoelectric energy harvesters are presented. Firstly, the electromechanical coupling model of cantilevered piezoelectric harvester was developed by considering nonlinearities of piezoelectric material, based on Hamilton theory, Rayleigh-Ritz method, Euler-Bernoulli beam theory and constant electrical field across the piezoelectric element. Then, the second order approximate solution of the primary response was investigated by using the method of multiple scales. The influences of piezoelectric material nonlinear and external excitation on system response, and load resistance on output power were analyzed. By exploring the nonlinear characteristics of the piezoelectric vibrator near the resonant frequency, the nature of the multi-solutions and jump phenomena in the resonance region has been revealed. The realization of primary resonance depends on the stability conditions and initial conditions. In addition, the generation power reaches the maximum by proper selections of resistance. Finally, numerical integral results verified the validity of the analysis.

导出引用

郭抗抗;;曹树谦;. 考虑材料非线性时压电发电悬臂梁的主共振响应分析[J]. 振动与冲击, 2014, 33(19): 8-16

GUO Kang-kang;CAO Shu-qian;. Primary Resonance of Piezoelectric Energy Harvesters Considering Nonlinearities of Piezoelectric Material[J]. Journal of Vibration and Shock, 2014, 33(19): 8-16