Fourier series expansion type of spectral collocation method for vibration analysis of cylindrical shells

An analysis method using a spectral collocation method for the vibration of cylindrical shells is proposed. Conventional spectral collocation methods have difficulty applying boundary conditions to fourth-order differential equations such as vibration equations of cylindrical shells. In this paper, an Hermite differentiation matrix is developed such that the proposed spectral collocation method can treat flexibly various boundary conditions. Since the vibration displacement of a cylindrical shell is periodic in the circumferential direction, it is solved semi-analytically using the Fourier series expansion. It is shown that the proposed method can offer more accurate solutions at a smaller number of unknowns, in less computation time and required memory than a finite element method.