基于区域分解的圆锥壳-圆柱壳-圆锥壳组合结构自由振动

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振动与冲击 ›› 2012, Vol. 31 ›› Issue (22) : 1-7.

论文

基于区域分解的圆锥壳-圆柱壳-圆锥壳组合结构自由振动

瞿叶高华宏星孟光谌勇龙新华

作者信息 +

A Domain Decomposition Method for Free Vibration Analysis of Joined Conical-Cylindrical-Conical Shells

Ye-gao QU Hong-xing HUA Guang MENG Yong CHEN Xin-hua LONG

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文章历史 +

摘要

提出了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。

Abstract

A domain decomposition approach is proposed for solving the free vibration of joined conical-cylindrical-conical shells (CCCSs), based on sub-domain generalized variational principle (SGVP) and least-squares weighted residual method (LSWRM). The CCCS is preliminarily divided into a cylindrical shell and two conical shells along the locations of the junctions; then these shell substructures are further decomposed into smaller cylindrical and conical shell segments to accommodate the computing requirements of high-order vibration modes. The constraint equations derived from interface continuity conditions between two adjacent shell segments can be incorporated into the system potential functional by means of the SGVP and LSWRM, which involves the reduction of conditional extremum problems to extremum problems without any constraints. Double mixed series, i.e. the Fourier series and Chebyshev orthogonal polynomials, are adopted as admissible displacement functions for each shell segment. To test the convergence, validity, efficiency and accuracy of the present method, numerical solutions are compared with those obtained using commercial program ANSYS. Very good agreement is observed, and the convergence rate of natural frequencies is shown to be very fast and the stability of the domain decomposition is very good.

导出引用

瞿叶高华宏星孟光谌勇龙新华. 基于区域分解的圆锥壳-圆柱壳-圆锥壳组合结构自由振动[J]. 振动与冲击, 2012, 31(22): 1-7

Ye-gao QU Hong-xing HUA Guang MENG Yong CHEN Xin-hua LONG. A Domain Decomposition Method for Free Vibration Analysis of Joined Conical-Cylindrical-Conical Shells[J]. Journal of Vibration and Shock, 2012, 31(22): 1-7