Computer simulation of forced oscillations of liquid in prismatic tank

Abstract

The method for simulating free and forced liquid vibrations in a prismatic tank is proposed. The liquid is supposed to be ideal, incompressible, and its current caused by applied loading is irrotational. The problem of force vibrations is solved by using the eigenmodes as basic functions. The resonance frequencies are defined. Thin-walled structure elements are wildly used in different engineering areas: chemical and aerospace industries, transportation, oil and gas producing. Usually these structures operate under intensive thermal and stress loadings and interact with the fluids located in their containers. These loadings can cause the destruction of thin shells containing dangerous liquids and can cause an ecological catastrophe. So the topical issue is estimating stress-strain characteristics, frequencies and modes of vibrations of such facilities. Liquid sloshing often occurs when the extreme loads are applied to the structure elements with compartments partially filled with different liquids. Vibration modes usually affect liquid sloshing modes, so the joint problem of fluid-structure interaction is crucial. Since there are no analytical solutions for tanks and reservoirs with complicated geometrical shapes, numerical methods have been employed for solving the linear boundary value problems of liquid sloshing in addition to the analytical ones. The presence of baffles can drastically change the dynamical behavior of fluid-filled structures as well. This paper is devoted to free and forced vibrations of cylindrical tanks filled with an incompressible ideal liquid. The dynamic analysis of shell structures is often performed by using finite and boundary element programs. The liquid pressure on the walls of the reservoir is defined by Cauchy-Lagrange integral. The external horizontal periodic loading is considered. The eigenvalues and the modes of free liquid vibrations in a prismatic tank have been obtained.