基于区域分解的薄壁回转壳自由振动分析  

Free vibration analysis of thin shells of revolution based on domain decomposition method

作　　者：瞿叶高[1] 孟光[1] 华宏星[1] 谌勇[1] 龙新华[1] 

机构地区：[1]上海交通大学机械系统与振动国家重点实验室,上海200240

出　　处：《应用力学学报》2013年第1期1-6,141,共6页Chinese Journal of Applied Mechanics

摘　　要：提出了一种区域分解法来分析不同组合边界条件的薄壁回转壳的自由振动。首先沿壳体母线方向将壳体分解为一些自由壳段,并采用广义变分和最小二乘加权残值法将壳体分区界面上的位移协调方程引入到壳体的势能泛函中;然后将壳段位移变量以Fourier级数和Chebyshev多项式展开,对总的势能泛函变分后得到回转壳的离散动力学方程。采用区域分解法分析了不同边界条件的圆柱壳、圆锥壳、抛物壳的自由振动,并将计算结果与其它文献值及ANSYS结果对比,结果表明:随着回转壳分区数目的增大,区域分解法计算出的壳体频率很快收敛;本文结果与其它方法计算结果非常吻合(相对误差不超过0.4%)。采用该方法可高效计算不同组合边界条件回转壳体的低阶和高阶振动频率。A domain decomposition approach is presented for free vibration analysis of thin shells of revolution subjected to different combinations of boundary conditions.The shell structure is divided into some free shell segments along the meridional direction of the shell,and all interface continuity constraints are incorporated into the system potential functional by means of a modified variational principle and least-squares weighted residual method.Double mixed series,i.e.the Fourier series and Chebyshev orthogonal polynomials,are adopted as assumed admissible displacement functions for each shell segment.By performing variational operation with respect to generalized coordinates,dynamic equations of motion for shells of revolution can be obtained.To test the convergence,efficiency and accuracy of the present method,typical shells of revolution,such as circular cylindrical,conical and parabolic shells,with different combinations of edge support conditions are examined.The numerical results obtained from the present method show good agreement with previously published results and those from the finite element program ANSYS,and the discrepancy is found to be very small and does not exceed 0.4% for the worst case.The convergence rate of natural frequencies is shown to be very fast and the stability of the present method is very good.The approach can be exploited to compute rapidly the effects of geometry and boundary conditions on the vibrations of thin shells of revolution.

关 键 词：广义变分 最小二乘加权残值法 自由振动 回转壳 

分 类 号：TH113[机械工程—机械设计及理论] TU33[建筑科学—结构工程]