COMPUTER MODELING LIQUID FORCED VIBRATIONS IN A PRISMATIC TANK

Abstract

The method to simulate 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 at intensive thermal and stress loadings, in interaction with fluids located in their containers. These loadings can cause the destruction of thin shells containing dangerous liquids that will be a reason of ecological catastrophe. So the topical issue here is a problem of estimation of stress-strain characteristics, frequencies and modes of vibrations of such facilities. Liquid sloshing often occurs when the extremely loads are applied to the structure elements with compartments partially filled with different liquids. Vibration modes are usually affected by liquid sloshing modes, so the coupled problem of fluidstructure interaction is crucial. Since analytic solutions do not exist for tanks and reservoirs with complicated geometrical shapes, in addition to the analytical methods, numerical methods have been employed for solutions of linear boundary value problems of liquid sloshing. Also the presence of baffles can drastically change the dynamical behaviour of fluid-filled structures. This paper is devoted to free and forced vibrations of prismatic and cylindrical tanks filled with an incompressible ideal liquid. The dynamic analysis of shell structures is often performed by use of 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 modes of free liquid vibrations in prismatic tank are obtained. The problem can be generalized in the case of the problem in non-linear formulation taking into account nonlinear components in Cauchy-Lagrange integral.