摘要
本文采用弹性圆锥扁壳中心无量纲振幅和壳体母线的倾角为参数，将挠度、应力函数的导数以及自由振动频率展开为双参量的幂级数形式．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答．从而给出弹性圆锥扁壳非线性自由振动频率的基本公式。
In this paper, the nondimensional amplitude in the centre of the elastic circular cone flat shell and the inclination of the generatrix of flat shell are used as the parameters to expand the derivatives of the stress and deflection functions with respect to the radiusand the frequency of the free vibration into dual parameter power series. Direct perturbation method is used to get every orders of recursive linear partial differential equations, and the variational method to get approximate solutions of these equations. Thus the fundamental formula of the nonlinear vibration frequency about elastic circular cone flat shell is obtained.
关键词
非线性振动
摄动法
扁壳
圆锥壳
nonlinear vibration
perturbation method/flat shell
