中文摘要：

基于压电非线性效应和位移非线性效应建立了压电驱动器非线性机电耦合动力学方程,应用Linz Ted-Poincaré法对弱非线性自由振动、接近共振时受迫振动及亚谐波振动响应方程进行推导,比较了压电驱动器在非线性及线性条件下响应的区别,使用四阶Runge-Kutta数值法和实验对理论推导进行了验证。结果表明：在两种非线性效应中,压电非线性对压电驱动器振动响应的影响是主要的;非线性数值解与解析解吻合较好,实验频率更接近非线性共振频率。

英文摘要：

On the basis of non-linear piezoelectric effect and non-linear displacement effect,the nonlinear electromechanical-coupled dynamic equations of piezoelectric actuator were established.Applying Linz Ted-Poincarémethod,response equations of weak nonlinear free vibration,force vibration near to natural frequency,subharmonic vibration were deduced.And the comparison between non-linear response and linear response was investigated.Using the fourth order Runge-Kutta and experimental method,the theoretical derivation was verified.Results show,in the two types of non-linear effects,the impact of piezoelectric non-linear effect on actuator is primary.Numerical results agree well with analytical solutions,and testing frequencies are close to non-linear resonance frequencies.