Sloshing in a horizontal cylindrical storage tank with a membrane cover on the surface of liquid

The liquid sloshing in a horizontal cylindrical storage tank with a membrane cover is investigated. The velocity potential theory is used for the flow and the linear elastic theory for the cover. For the former the Bessel-Fourier expansion is used. The expansion automatically satisfies the governing equation and the body surface condition of the flat ends. The deflections of the membrane are expanded into a cosine series together with a Bessel series. These expansions are then matched through the dynamic and kinematic equations of the membrane and the body surface boundary conditions of the shell, and the problem is completed by imposing the edge conditions of the membrane. Through the combined matrix equation, the natural frequencies are obtained through finding the zero points of the determinant of the matrix. The problem of the forced motion at the excitation frequency is then solved, where the inhomogeneous boundary condition is also expanded into the Bessel series. Extensive results are obtained and their physics and implications are discussed. It is found that the properties of the membrane will exert noticeable effects on the distribution of natural frequencies, and subsequently affect the possibility of the resonance.