基于区域分解的组合结构振动分析方法

上海交通大学学报（自然版） ›› 2012, Vol. 46 ›› Issue (09): 1487-1492.

基于区域分解的组合结构振动分析方法

瞿叶高，华宏星，孟光，谌勇，龙新华

(上海交通大学机械系统与振动国家重点实验室, 上海 200240)

收稿日期:2011-10-21 出版日期:2012-09-28 发布日期:2012-09-28

A Domain Decomposition Approach for Vibration Analysis of Joined Structures

QU Ye-Gao, HUA Hong-Xing, MENG Guang, CHEN Yong, LONG Xin-Hua

(State Key Laboratory of Mechanical System and Vibration, Shanghai Jiaotong University, Shanghai 200240, China)

Received:2011-10-21 Online:2012-09-28 Published:2012-09-28

摘要/Abstract

摘要： 提出了一种分析一般边界条件下组合结构动力学特性的区域分解法.首先，沿组合结构连接处和位移边界而将组合结构分解成若干自由子结构，并将子结构分解为一些规则子域，以获取组合结构的高阶振动特性；采用分区广义变分和最小二乘加权残值法将子域界面的位移协调方程引入组合结构的能量泛函中，以使组合结构的动力分析问题归结为在满足分区界面位移协调条件下的无约束泛函变分问题.同时，采用区域分解法分析了不同边界条件的圆锥壳环肋骨圆柱壳圆锥壳组合结构的动力学特性，通过与有限元软件ANSYS的相应结果进行对比，验证了其计算精度和稳定性.结果表明，所提出的区域分解法具有高效率、高精度和良好收敛性等优点.

关键词: 区域分解, 分区广义变分, 最小二乘加权残值法, 组合结构, 振动分析

Abstract: A domain decomposition approach was proposed for vibration analysis of joined structures with general boundary conditions. The joined structure is preliminarily divided into several substructures along the locations of the junctions and the prescribeddisplacement boundaries; then these substructures are further decomposed into regular subdomains to accommodate the computing requirement of highorder vibration modes. The constraint equations derived from interface continuity conditions between two adjacent subdomains are incorporated into the system energy functional by means of a subdomain generalized variational principle and leastsquares weighted residual method, which involves the reduction of conditional extremum problems to extremum problems without any constraints. To test the convergence, efficiency and accuracy of the present method, a typical joined conicalcylindricalconical shell with ring stiffeners was examined. Numerical solutions for natural frequency and dynamical response of the joined shell were compared with those obtained using the finite element program ANSYS. The present solution is found to be very efficient, robust and accurate. Key words：

Key words: domain decomposition, subdomain generalized variational, least-squares weighted residual method, joined structure, vibration analysis

中图分类号:

TH 113
TU 33

瞿叶高, 华宏星, 孟光, 谌勇, 龙新华. 基于区域分解的组合结构振动分析方法 [J]. 上海交通大学学报（自然版）, 2012, 46(09): 1487-1492.

QU Ye-Gao, HUA Hong-Xing, MENG Guang, CHEN Yong, LONG Xin-Hua. A Domain Decomposition Approach for Vibration Analysis of Joined Structures[J]. Journal of Shanghai Jiaotong University, 2012, 46(09): 1487-1492.

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