Abstract
The coupled problem of liquid sloshing in a tank with a membrane cover and elastic side walls is investigated. The velocity potential theory is used for the flow and the linear elastic theory for the cover and side walls. For the former, the vertical mode expansion is used, in which all the roots of the dispersion relationship are first found. The expansion automatically satisfies the governing equation, the tank bottom, and the tank cover conditions. The deflections of the side walls are expanded into a cosine series together with a four term polynomial, which is vital for the procedure to succeed. These expansions are then matched through the dynamic and kinematic equations of the plates, and the problem is completed by imposing the edge conditions of the plate and membrane. Through the combined matrix equation, the natural frequencies of the system are obtained. In addition, the nature of the dispersion relationship of the membrane is analyzed. Explicit solutions are obtained for some special cases, and the link with the free surface sloshing is established. Extensive numerical results are provided, and their physics is analyzed.
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