采用参数摄动及有限差分法研究了外周边作用均布面内压力、内周边固连一刚性质量块、且受横向弹性支承的各向同性环形薄板的轴对称大振幅自由振动和稳定性问题,计算出用中心振幅表示的非线性固有频率的高次摄动解,并求出了表征环板面内失稳特征的临界压力。 The parametric perturbations and finite difference methods were used to study the large-amplitude free vibration and stability of axisymmetrical annular thin plates subjected to uniform pressure in the outer periphery, rigid masses in the inner periphery, and transverse elastic support. Calculate the high-order perturbation solution of the nonlinear natural frequency expressed by the center amplitude, and determine the critical pressure that characterizes the in-plane instability of the ring plate.