Su Zhu, Jin Guoyong
College of Power and Energy Engineering, Harbin Engineering University, Harbin, 150001, People's Republic of China.
J Acoust Soc Am. 2016 Nov;140(5):3925. doi: 10.1121/1.4967853.
This paper presents a Fourier spectral element method (FSEM) to analyze the free vibration of conical-cylindrical-spherical shells with arbitrary boundary conditions. Cylindrical-conical and cylindrical-spherical shells as special cases are also considered. In this method, each fundamental shell component (i.e., cylindrical, conical, and spherical shells) is divided into appropriate elements. The variational principle in conjunction with first-order shear deformation shell theory is employed to model the shell elements. Since the displacement and rotation components of each element are expressed as a linear superposition of nodeless Fourier sine functions and nodal Lagrangian polynomials, the global equations of the coupled shell structure can be obtained by adopting the assembly procedure. The Fourier sine series in the displacement field is introduced to enhance the accuracy and convergence of the solution. Numerical results show that the FSEM can be effectively applied to vibration analysis of the coupled shell structures. Numerous results for coupled shell structures with general boundary conditions are presented. Furthermore, the effects of geometric parameters and boundary conditions on the frequencies are investigated.
本文提出了一种傅里叶谱元法（FSEM），用于分析具有任意边界条件的圆锥 - 圆柱 - 球形壳的自由振动。还考虑了圆柱 - 圆锥壳和圆柱 - 球形壳这两种特殊情况。在该方法中，每个基本壳组件（即圆柱壳、圆锥壳和球形壳）被划分为适当的单元。采用变分原理结合一阶剪切变形壳理论对壳单元进行建模。由于每个单元的位移和旋转分量表示为无节点傅里叶正弦函数和节点拉格朗日多项式的线性叠加，因此通过采用组装过程可得到耦合壳结构的整体方程。位移场中引入傅里叶正弦级数以提高解的精度和收敛性。数值结果表明，傅里叶谱元法可有效应用于耦合壳结构的振动分析。给出了具有一般边界条件的耦合壳结构的大量结果。此外，研究了几何参数和边界条件对频率的影响。
