基于谐波平衡法的双稳态压电发电系统非线性振动特性研究

Non-linear vibration analysis of bistable piezoelectric power generation system based on harmonic balance method

研究双稳态压电发电系统非线性振动特性。通过谐波平衡法计算获得系统幅频响应方程,分析不同非线性系数、阻抗参数与激励对系统幅值解影响,随激励频率、幅值的变化,双稳态压电发电系统幅值解存在跳跃、多解现象,调节非线性系数及阻抗参数可使不稳定区域范围最小;研究外加激励对功率影响,随非线性系数及阻抗参数的增加,输出功率先增加后减小,通过调节磁化强度与负载阻抗可使系统输出功率最大;通过实验所得频率电压响应曲线及电阻功率响应曲线,验证系统非线性分析结果。可为双稳态压电发电系统工程应用提供理论依据。

The nonlinear vibration characters of bistable piezoelectric power generation system were investigated. Adopting the harmonic balance method,the equation of amplitude-frequency response was derived.The effects of different nonlinear coefficients,impedance parameters and excitations were analyzed.With the change of frequency and force amplitude,the jump and multiple solutions phenomenon were observed.The minimum unstable area was obtained by varying the nonlinear coefficient and impedance parameters.Then,the influence of excitation on the power was analyzed. With the increase of nonlinear coefficient and impedance parameters,the output power first increases and then decreases. The maximum power was got by adjusting the magnetization and the load impedance.The voltage frequency response curves and the power resistance response curves obtained by experiments verify the system’s nonlinear characters.The results provide theoretical evidence for the engineering application of bistable piezoelectric power generation system.