摘要
分析了各向同性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·卡门的板理论方程其有同样的精度。文中采用双重富氏级数法及伽辽金方法近似地求解运行方程，利用谐波平衡法和牛顿－莱福逊法求解高度耦合的非线性微分方程组，分析了模式的耦合对非线性频率的影响。结果表明，对于较小的振幅－厚度比，单模式解答能给出较准确的结果。而对于较大的振幅－厚度比，就应该进行多模式分析。
In this paper, the multimode analysis of nonlinear free flexural vibrations of circular cylindrical isotropic shells with simply supported edges is presented. The equations of motion of circular cylindrical shells for large amplitude flexural vibrations are deduced by the classical nonlinear elastic mechanics method. The static version of these equations are of the same approximation as those of the von Karman plate theory. Double Fourier series method and Galerkins method are used to solve the govering equations approximatively, the method of harmonic balance and the Newton Raphson method are used to solve the highly coupled ordinary differential equations. The effect of coupling of vibrating modes on the nonlinear frequency is analysed. The result shows that, for small values of amplitude the effect of coupling of vibrating modes on the nonlinear frequency is less signficant, but for large values of amplitude the effect of coupling of vibrating modes on the nonlinear frequency should be considered. In the frequency analysis a hardening type of nonlinearity is observed.
出处
《应用力学学报》
EI
CAS
CSCD
北大核心
1997年第1期5-10,共6页
Chinese Journal of Applied Mechanics
关键词
非线性
多重模式
非线性频率
圆柱壳
nonlinear, multimode, coupling, nonlinear frequency.
