受静载作用的柔韧圆板的非线性固有频率

Nonlinear natural frequencies of flexible circularplates subjected to static loads

研究了中心集中静载作用下圆薄板的非线性自由振动问题．其静平衡问题采用小挠度解，在此基础上，引入Ｇｒｅｅｎ函数，将动力协调方程及对应的边界条件化为等价的积分方程，并把摄动变办法应用于动力平衡方程，求得了以静载荷为参数的最低固有频率与中心最大振幅间的特征关系．

Nonlinear free vibration of circular plates under the central concentrated static loads is studied.The small deflection solutions are given for the static equilibrium problems.Based on this and by introducing Green's function,dynamic compatible equation and corresponding boundary conditions are transformed into a equivalent integral equation and using perturbation variational method to dynamic equilibrium equation and taking static load as the parameter,the characteristic relation between the least natural frequency and central maximum amplitude is obtained.