Free vibration analysis of a cylindrical shell eccentrically coupled with a fluid-filled vessel

A theoretical study is presented on the free vibration of a horizontally guided, circular cylindrical shell eccentrically submerged in a fluid-filled rigid vessel. In the analysis, it is assumed that the interior and annulus cavities of the shell are filled with an ideal fluid. The Donnell–Mushtari's shell equations and the velocity potential for fluid motion are used for theoretical formulation. In order to define an eccentricity between the axes of the shell and the vessel, an additional shifted coordinate system is introduced. In the theoretical formulation, it is necessary that the fluid motion is described by the modified Bessel functions in the shifted coordinates. Hence, the Beltrami's theorem is used for the translated forms of the modified Bessel functions. The theoretical results show that the eccentricity reduces the coupled natural frequencies for all axial and circumferential modes. Additionally, the so-called non-dimensional added virtual mass incremental factor that reflects the increase of kinetic energy due to the fluid motion is analytically obtained as a function of the eccentricity and modes of vibration.