摘要
提出一种分区广义变分和最小二乘加权残值区域分解法来分析圆锥壳-圆柱壳-圆锥壳组合结构的自由振动。首先将组合结构分解为圆柱壳、圆锥壳子结构,为获取组合壳体的高阶振动特性,进一步将圆柱壳、圆锥壳子结构分解为圆柱壳段和圆锥壳段。采用分区广义变分和最小二乘加权残值法将各壳段分区界面上的位移和转角协调方程引入到组合壳体的势能泛函中,使组合壳体的振动分析问题,归结为在满足分区界面位移和转角协调条件下的无约束泛函变分问题。圆柱壳段及圆锥壳段位移变量的周向和轴向(或母线方向)分量分别以Fourier级数和Chebyshev多项式展开。将区域分解法计算出的组合壳体振动频率与有限元软件ANSYS结果进行对比发现,两者非常吻合,验证了区域分解方法的收敛性和计算精度。
A domain decomposition approach was proposed for solving free vibration of a joined conical-cylindrical-conical shell （CCCS）, based on sub-domain generalized variational principle （SGVP） and least-square weighted residual method （LSWRM）. The CCCS was preliminarily divided into a cylindrical shell and two conical shells along the locations of junctions, then these shell substructures were further decomposed into smaller cylindrical and conical shell segments to meet the computing requirements of high-order vibration modes. The constraint equations derived from interface continuity conditions between two adjacent shell segments could be incorporated into the system potential functional by means of SGVP and LSWRM, they changed a conditional extremum problem into an extremum problem without any constraints. Double mixed series, i. e., Fourier series and Chebyshev orthogonal polynomials, were adopted as admissible displacement functions for each shell segment. To test the convergence, validity, efficiency and accuracy of the presented method, numerical results were compared with those obtained using the commercial soft ware ANSYS. Very good agreement was observed, and the convergence rate of the natural frequencies of the structure was shown to be very fast and the stability of the domain decomposition was very good.
出处
《振动与冲击》
EI
CSCD
北大核心
2012年第22期1-7,共7页
Journal of Vibration and Shock
关键词
区域分解
分区广义变分
最小二乘加权残值
圆锥壳-圆柱壳-圆锥壳组合壳体
自由振动
domain decomposition
sub-domain generalized variational principle
least-square weighted residual method
joined conical-cylindrical-conical shell
free vibration
