Vibration of fluid-coupled coaxial cylindrical shell under horizontal excitation

Two coaxial circular cylindrical shells with the same height are partially filled with an incompressible inviscid fluid to the same depth in the inner shell and in the outer annular gap between them. The outer shell is rigid, the inner is elastic. The shells’ bottom is an absolutely rigid plate fixed on a shaking table, which can generate sinusoidal horizontal excitation. The problem is to derive the governing equations considering the dynamic fluid-structure interaction of this system under a horizontal sinusoidal and/or seismic excitation. Under the assumption of harmonic behavior of the fluid and shell in the time domain, the fluid equations are solved using a standard technique of separation of variables and the Fourier series expansion for the corresponding boundary conditions. The principle of virtual work statement for a structure subjected to hydrodynamic loads due to an inviscid, incompressible liquid is used and a Galerkin discretization is made.