摘要
应用Donnell’s简化壳理论,在考虑阻尼和几何非线性的情况下,基于Galerkin方法,对旋转的薄壁悬臂圆柱壳在法向激振力作用下的非线性行波振动进行了数值分析。在研究过程中,首先,考虑阻尼并引入几何非线性项,建立薄壁圆柱壳的非线性波动方程,然后,采用Galerkin方法对波动方程进行转换,选取不同的模态组合,得到相应模态坐标下的非线性微分方程,最后用Runge?Kutta法进行数值计算并对圆柱壳的非线性波动振动特性进行了分析。结果表明,几何非线性使圆柱壳呈现明显的硬特性,其硬特性随激振力幅值的增大而得到加强,共振区存在多值性,多模态分析表明,轴向二阶模态对主模态影响较大,计算时宜采用两个轴向模态。
A numerical analysis was made to study the nonlinear travelling wave vibration of a cantilever rotating thin cylindrical shell under the action of a normal exciting force,taking damping and geometric nonlinearities into account,using Donnell's shallow shell theory and based on Galerkin's method.In the analysis,a nonlinear wave vibration equation of the thin cylindrical shell including damping and items due to geometric nonlinearities was established and then transformed by Galerkin's method.With different combinations of modes different nonlinear differential equations in modal coordinates were obtained.The Runge Kutta method was used to solve the equations numerically and some features of nonlinear wave vibration were discussed.The results show that geometric nonlinearities make the cylindrical shell display a hardening behavior and the behavior will be intensified with the increase of magnitude of exciting force.Multivalue phenomenon occurs in resonance regions.Multimode analysis shows that the axial mode of second order is of strong effect on the main mode and two axial modes should be considered in the computation.
出处
《振动与冲击》
EI
CSCD
北大核心
2008年第12期9-12,22,共5页
Journal of Vibration and Shock
基金
国家自然科学基金
上海宝钢集团公司联合资助(50574019)
关键词
行波振动
几何非线性
模态坐标
主模态
轴向模态
travelling wave vibration
geometric nonlinearity
mode coordinate
main mode
axial mode
