静载荷作用下扁球壳轴对称非线性自由振动

研究了扁球壳在静载荷作用下的轴对称非线性自由振动问题。根据扁球壳非线性动力变分方程，运用修正迭代法给出非线性静力边值问题的一次近似解析解，应用Ｇａｌｅｒｋｉｎ技术得到了关于时间部分的非线性动力方程，用Ｌｉｎｄｓｔｅｄｔ－ｐｏｉｎｃａｒé摄动法获得了以静载荷为参数的非线性固有频率与振幅间的特征关系，并以图表的形给出算例．本文的退化结果，可直接得到圆薄板轴对称非线性自由振动的有关结论．

Axisymmetric Nonlinear Free Vibration of Shallow Spherical Shells Subjected to Static Loads

The objective of this paper is to study the nonlinear free vibration of shallowspherical shells under static loads. According to the nonlinear dynamic variational equationof shallow spherical shells and using the modified iteration method,the first-order approxi-mate analytical solution are given first of all as a solution to static nonlinear boundary prob-lem. Based on the static solutions,the Galerkin's error minimizing technique is used to de-velop dynamic equation for the unknow functions in time domain only. Finally,the charac-terstic relation between nonlinear natural frequency and the amplitude under the static loadsas the parameter is derived using Lindstedt-poincare perturbation method.The results aregiven in form of figure and table in illustration of subject matter.It can be applied directly todraw some relevant conclusions on the problems of the nonlinear free vibriation of circularthin plates as a degenerated characteristic relation above obtained in this paper.