Free and forced vibration characteristics of submerged finite elliptic cylindrical shell

In this paper, an analytical method to study the free and forced vibration behaviors of a submerged finite elliptic cylindrical shell is proposed. The vibration equations are derived based on Flügge shell theory. Unlike the vibration equations of a circular cylindrical shell, the coefficients of state variables in the vibration equations of the elliptic cylindrical shell are variable with the circumferential curvature, which causes that the vibration equations are rather difficult to solve. To solve this problem, the shell's displacements are expanded in double Fourier series in the view of wave propagation and the circumferential curvature is expanded in single Fourier series. The partial differential equations with variable coefficients are converted into a set of linear equations which couple with each other about the circumferential modal parameters. The fluid around the shell is considered as an ideal acoustic medium and the sound pressure is described by the Helmholtz Equation. Free and forced vibration responses of the submerged finite elliptic cylindrical shell are obtained by solving the coupled equations and are also compared with those of circular cylindrical shell and infinite elliptic cylindrical shell. The present results show good agreements with published results and FEM results. The influences of main parameters of the shell, such as ellipticity parameter, shell thickness ratio, shell length ratio and exciting force's position, on the vibration characteristics are also discussed in detail.