圆柱壳的非线性自由振动分析

Analysis of Nonlinear Free Vibrations of Circular Cylindrical Shells

本文分析了各向同性封闭圆柱壳的非线性自由振动。文中采用经典的非线性弹性力学方法推导了圆柱壳的大振幅运动方程,这些方程的静态形式与冯·卡门的板理论方程具有同样的精度。文中讨论了四种基本振动模态,并且还以数学公式的形式给出了一般的最终结果,一些例子以曲线给出结果,并进行了比较。结果还表明线性振动可以作为非线性振动的一种特例。

In this paper, nonlinear free flexural vibrations analysis of closed circular cylindrical isotropic shells are presented. The equations of motion of circular cylindrical shell for large amplitude flexural vibrations are deduced in the classical nonlinear elastic mechanics method. The static versions of these equations are of the same approximation as those of the von Karman plate theory. Four fundamental vibrating modes are discussed, and the results ate given in form of mathematical formula and some examples are given in figures. The linear vibrations are treated as a special case of nonlinear vibrations.