周边嵌入弹性圆薄板非线性自由振动直接摄动解法

采用弹性圆薄板中心无量纲振幅和板厚与半径的比值为参数。将挠度、应力函数对半径的导数以及自由振动频率展开为双参数的幂级数。用直接摄动法获得各级递推线性偏微分方程。应用变分法求得各级递推方程的近似解，从而给出弹性圆薄板非线性自由振动频率的基本公式。

Direct perturbation method of nonlinear vibration for the elastic circular thin plate

In this paper, the nondimensional amplitud in the centre of the elastic circular thin plate and the ratio of the thickness to the radius are used as the parameters to expand the derivatives of the stress and deflection functions with respect to the radius and the frequency of the free vibration into dualparameter power series. Direct perturbation method is used to get every orders of recursive linear portial differential equations, and the variational method to get approximate solutions of these equations. Thus the fundamental formula of the nonlinear vibrations frequency about elastic circular thin plate is obtained.