中文摘要：

研究了参数激励压电梁的振动稳定性，考虑非线性阻尼的影响，采用Hamilton变分原理推导结构运动方程，采用多尺度法求解稳态响应幅值。通过数值算例分析了电压、轴向力以及非线性阻尼等因素对定常解稳定性的影响。通过分析可见，外加电压与压电层上下表面电势差的差值△V主要影响自变量σ／ω的取值区间，对定常解的稳定性影响较小；梁所承受的轴力越小，定常解稳定区间越大；非线性阻尼的常数项和二次项系数越大，定常解稳定区间越大。

英文摘要：

Considering the effects of nonlinear damping, the vibration stability of the parametrically excited piezoelectric beams is studied. The Hamilton principle is applied to derive the equation of motion and the method of multiple scales is used to solve the amplitude values of the stationary response. The numerical example is given to analyze the effects of the voltage, axial force and nonlinear damping on the stability of the steady solution. From the results that the difference △V between the applied outer voltage and the electric potential deference between the upper and lower surfaces of the piezoelectric layer mainly affects the range of the independent variable σ/ω and has slight effects on the stability of the steady solution; the smaller the axial force, the larger the stable regions of the steady solution ; and the larger the constant and quadratic terms of the nonlinear damping, the larger the stable regions of the steady solution.