Dynamic Analysis of General Rotationally Symmetric Built-Up Structures Using a Modified Fourier Spectral Element Approach

A modified Fourier spectral element method (SEM) is developed to study vibration behaviors of general built-up systems that consist of various rotationally symmetric structures, including conical, cylindrical, and spherical shells, and annular plates. The substructures are formulated as spectral elements based on the type of elementary structure. These spectral elements can be easily assembled using three-dimensional elastic couplers at the interfaces to coordinate the forces and moments of adjacent substructures with respect to a cylindrical coordinate system. A modified Fourier series that can adapt general coupling and boundary conditions is used to describe the displacement components of each spectral element. The generalized variation of the expansion coefficients yields the vibration equations of the built-up system. The convergence and accuracy of the method are validated through several numerical examples for various shell and plate combinations. The dynamic behaviors of the rotationally symmetric built-up structures are investigated by modal and forced vibration analysis. The method can predict the vibration responses of rotationally symmetric, built-up structures with low computational cost.