圆板在周边面内载荷作用下的非线性振动

Nonlinear Vibration of Circular Plates Subjected to a Peripheral Inplane Load

本文采用摄动变分法讨论了边界横向夹紧、中面内有均布载荷作用的圆形薄板的非线性自由振动问题。求出了与面内载荷有关的圆板的近似线性和非线性固有频率,并给出了不同载荷参数下的特征曲线。结果表明,线性问题的临界压力是保守的,而当压力超出临界压力一定范围时,圆板的非线性固有频率仍有意义。

This paper deals with the nonlinear free vibration of a thin circular plate subjected uniformly to an inplane pressure around the boundary. The approximations of the linear and nonlinear natural frequencies of the plate which are relate to the inplane pressure are calculated by perturbation-variation method. For some given load parameters,the eigenvalue curves are plotted. It can be found from the results that the critical pressure of the linearized problem is conservative due to the nonlinear natural frequency being still positive when the inplane pressure is greater than the critical pressure.