复合材料旋转壳自由振动分析的新方法

A NEW METHOD FOR FREE VIBRATION ANALYSIS OF COMPOSITE LAMINATED SHELLES OF REVOLUTION

提出了一种半解析区域分解法来分析任意边界条件的复合材料层合旋转壳自由振动.沿壳体旋转轴线将壳体分解为一些自由的层合壳段,视位移边界界面为一种特殊的分区界面;采用分区广义变分和最小二乘加权残值法将壳体所有分区界面上的位移协调方程引入到壳体的能量泛函中,使层合壳的振动分析问题归结为无约束泛函变分问题.层合壳段位移变量采用Fourier级数和Chebyshev多项式展开.以不同边界条件的层合圆柱壳、圆锥壳及球壳为例,采用区域分解法分析了其自由振动,并将计算结果与其他文献值进行了对比.算例表明,该方法具有高效率、高精度和收敛性好等优点.

A semi-analytical domain decomposition approach is proposed for free vibration analysis of laminated com- posite shells of revolution subjected to arbitrary boundary conditions. A laminated shell structure is divided into some shell segments along the axis of revolution. The geometrical boundaries are treated as special interfaces as those between two adjacent shell segments. All interface continuity constraints are incorporated into the system potential functional by means of a subdomain generalized 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. In order to validate the proposed formulation, typical laminated shells of revolution, such as circular cylindrical, conical and spherical shells, with various combinations of edge support conditions, are examined. The numerical results obtained from the present method show good agreement with previously published results. The present solution is very efficient, robust and accurate. The computational advantage of the approach can be exploited to gather useful and rapid information about the effects of geometry and boundary conditions on the vibrations of laminated composite shells of revolution.