正交铺设复合材料层合圆柱壳自由振动分析的辛空间波方法  

Symplectic wave-based method for the free vibration analysis of cross-ply composite laminated circular cylindrical shells

作　　者：韩少燕 李榆银 高汝鑫 HAN Shaoyan;LI Yuyin;GAO Ruxin(Department of Mechanical Engineering,Xi’an Jiaotong University City College,Xi’an 710018,China;Zhuzhou CRRC Times Electric Co.,Ltd.,Zhuzhou 412001,China;Institute of Advanced Structure Technology,Beijing Institute of Technology,Beijing 100081,China;State Key Laboratory of Structural Analysis for Industrial Equipment,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]西安交通大学城市学院机械工程系,西安710018 [2]株洲中车时代电气股份有限公司,湖南株洲412001 [3]北京理工大学先进结构技术研究院,北京100081 [4]大连理工大学工业装备结构分析国家重点实验室,大连116024

出　　处：《振动与冲击》2024年第6期113-120,共8页Journal of Vibration and Shock

基　　金：国家自然科学基金青年项目(12102045);工业装备结构分析国家重点实验室开放课题(GZ21110)。

摘　　要：针对正交铺设复合材料层合圆柱壳的自由振动分析,提出了基于辛空间的波方法。首先基于Kirchhoff-Love薄壳理论,选取合适的状态向量,推导了复合材料层合圆柱壳在辛体系中的振动控制方程;其次利用分离变量法将正交铺设复合材料层合圆柱壳的自由振动问题转化为Hamilton体系下的辛本征值问题;最后根据辛空间波形与圆柱壳模态的对应关系,得到不同边界条件下的自由振动波数,进而得到圆柱壳自由振动问题的代数方程组,求解即可得到正交铺设复合材料层合圆柱壳的固有频率和模态。数值算例对比了该方法和其他方法计算得到的圆柱壳固有频率,验证了该方法的有效性和准确性。A symplectic wave-based method was proposed for the free vibration analysis of cross-ply laminated cylindrical shells with arbitrary boundary conditions.First,based on the Kirchhoff-Love’s shell theory,the governing equation of a cross-ply laminated cylindrical shell was established in the symplectic duality system by selecting an appropriate state vector.Secondly,the characteristic equation for the cross-ply composite laminated cylindrical shell was derived so that the symplectic eigenproblem could be formed.Finally,the symplectic eigensolution was substituted into the boundary conditions at both ends of the cylindrical shell,and the algebraic equation of the free vibration problem of the cylindrical shell was obtained and then solved to give the natural frequencies and modals of the cross-ply composite laminated cylindrical shell.Numerical examples were given to show the validity and accuracy of the present method through comparing the results obtained using the present and other methods.

关 键 词：层合圆柱壳 正交铺设 自由振动 辛空间 基于波的方法 

分 类 号：O327[理学—一般力学与力学基础]