Dynamics of a concentrically or eccentrically submerged circular cylindrical shell in a fluid-filled container

Abstract A theoretical study is presented on the natural frequencies of a circular cylindrical shell concentrically or eccentrically submerged in a fluid-filled rigid cylindrical container. In this analysis, it is assumed that the shell is clamped at both ends, and an annulus between the shell and the rigid container is filled with a non-viscous and compressible fluid. The velocity potential for fluid motion is formulated in terms of Fourier series expansion, and the modal displacements of the shell are expanded with the finite Fourier series using the finite Fourier transformation. Along the contacting surface between the shell and fluid, the compatibility requirement is applied for fluid–structure interaction. In order to consider eccentricity between the axes of the shell and the container, an additional shifted co-ordinate system is introduced. Graf's additional theorem and Beltrami's theorem are used for the translated forms of the Bessel functions in the shifted co-ordinate system. The proposed analytical method for the concentrically submerged shell is verified by observing an excellent agreement with the finite-element analysis results. In order to evaluate the dynamic characteristics of the fluid-coupled system, the effects of annular fluid gap and eccentricity of the shell on the natural frequencies are investigated.