圆柱壳-圆锥壳组合结构振动分析的新方法  

A NEW METHOD FOR VIBRATION ANALYSIS OF JOINED CYLINDRICAL-CONICAL SHELLS

作　　者：瞿叶高[1] 华宏星[1] 孟光[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：《工程力学》2013年第3期24-31,共8页Engineering Mechanics

摘　　要：提出了一种区域分解法来分析不同边界条件下圆锥壳-圆柱壳-圆锥壳组合结构的自由振动和强迫振动特性。首先将组合壳体的位移边界与固定边界分开,将其分解为圆柱壳、圆锥壳子结构;为能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自由的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。圆柱壳段和圆锥壳段位移变量的周向和轴向分量分别采用Fourier级数和Chebyshev多项式展开。算例表明:区域分解法计算出的不同边界条件下组合壳体自由振动和强迫振动结果与有限元软件ANSYS结果非常吻合;该方法具有高效率、高精度和收敛性好等优点。A domain decomposition approach is proposed for solving the free and forced vibration of joined conical-cylindrical-conical shell （CCCS） structures with different boundary conditions. The CCCS is preliminarily divided into cylindrical and conical shell substructures along the locations of the junctions and the prescribed-displacement boundaries; then these shell substructures are further decomposed into smaller cylindrical and conical shell segments to accommodate the computing requirement of high-order vibration modes and responses. The constraint equations derived from all interface continuity conditions are incorporated into the system energy function by means of the subdomain generalized variational principle and the least-squares weighted residual method, 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 assumed admissible displacement functions for each shell segment. To test the convergence, efficiency and accuracy of the present method, free and forced vibration solutions for CCCSs with different boundary conditions are compared with those obtained using finite elment program ANSYS. Good agreement is observed and the present solution is found to be very efficient, robust and accurate.

关 键 词：区域分解 分区广义变分 最小二乘加权残值 圆柱壳-圆锥壳组合壳体 自由振动 强迫振动 

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