摘要
圆薄板控制方程复杂、边界挠性不易描述,边界挠性对圆薄板动态特性的影响规律研究尚不充分。本文采用Hamilton变分原理建立了挠性边界圆薄板的动力学方程;采用Fourier级数描述边界挠性,应用Galerkin方法对其简化;利用小参数摄动分析获得了挠性边界圆薄板固有频率的半解析式。本文给出的圆薄板固有频率半解析结果表明:边界挠性可使圆板固有频率降低;挠性参数的均值对固有频率的影响最大。本文研究可为圆薄板边界的模拟设计提供参考。
In order to study the effects of the flexible boundary on the dynamic characteristics of the circular thin plate, the dynamic equation is derived by employing the Hamilton variational principle in the paper. In the equation the flexible boundary is described by the Fourier series and simplified by Galerkin method. The natural frequencies are obtained by the perturbation analysis with small parameters. The semi-analytic results are helpful for realizing the effects of the flexible boundary, that is, the natural frequency is decreased subjected to the flexible boundary, and the mean value of the flexible parameter has a greater effect on the natural frequency of the circular thin plate. And, the results provide reference to the design on the boundaries of the circular thin plate.
出处
《应用力学学报》
CAS
CSCD
北大核心
2014年第5期667-670,825,共5页
Chinese Journal of Applied Mechanics
基金
国家自然科学基金委员会-中国工程物理研究院联合基金资助项目(NSAF10876100)
