圆锥壳-圆柱壳-球壳组合结构自由振动分析

基于Reissner薄壳理论，采用区域分解法分析了不同边界条件下圆锥壳-圆柱壳-球壳组合结构的自由振动。首先在壳体连接处将组合壳体分为独立的圆锥壳、圆柱壳和球壳，并将各个子壳体沿旋转轴线分解为若干自由壳段；然后将所有壳段分区界面(包括边界界面)的位移协调方程通过分区广义变分和最小二乘加权残值法引入到组合壳体的能量泛函中；最后将壳段位移场变量的周向分量和轴向分量分别以Fourier级数和Chebyshev多项式展开，通过变分后得到整个组合壳体的离散动力学方程。将区域分解法计算结果与有限元软件ANSYS计算结果进行对比，验证了区域分解法在分析圆锥壳-圆柱壳-球壳组合结构自由振动的正确性和计算精度，并分析了组合壳体长径比及厚径比对自由振动频率的影响。

Free vibration analysis of joined conical-cylindrical-spherical shells

Based upon the Reissner’s thin shell theory, the free vibration of the joined conical-cylindrical-spherical shell with different boundary conditions was analyzed with a domain decomposition method. The joined shell was first divided into independent conical, cylindrical and spherical shell substructures along the junctions, and then these substructures were further decomposed into smaller shell segments along the axis of revolution. The constraint equations derived from interface continuity conditions between two adjacent shell segments (including boundary conditions) were introduced into the energy functional of the joined shell via a modified generalized variational principle and least-squares weighted residual method. The Fourier series and Chebyshev orthogonal polynomial were employed as the admissible displacement functions for each shell segment in order to obtain the discretized equations of motion of the joined shell. The natural frequencies were calculated and compared with those derived from the finite element software ANSYS to confirm the reliability and accuracy of the analytical solution. Finally, the influence of the length-to-radius ratio and the thickness-to-radius ratio on the free vibrational behavior of the joined shell structure was investigated.