Liquid vibrations in circular cylindrical tanks with and without baffles under horizontal and vertical excitations

Abstract

The paper is devoted to issues of numerical simulation of free surface elevations in rigid circular cylindrical fluid-filled tanks under external vertical and horizontal loadings with usage boundary element methods. The liquid in reservoirs is assumed to be ideal and incompressible, and its flow is irrotational. The influence of horizontal and vertical baffle installation is considered and damping effects due baffles are estimated. The influence of elasticity effects is considered. Free, forced and parametrical vibrations are examined. Modes of the free liquid vibrations present basic functions for analysis of forced and parametric vibrations. The modes and frequencies of the free liquid vibrations in baffled and un-baffled circular cylindrical tanks are received by using single- and multi-domain boundary element methods. The new effective procedure is developed for numerical solution of resolving system of singular integral equations. The problems of forced vibrations are reduced to solving the systems of second order ordinary differential equations. For parametric vibrations the system of Mathieu equations with non-zero right-hand parts is obtained. The numerical simulation of different kinds of loadings and baffle configurations is accomplished. The instability conditions of the fluid-filled tank subjected to both horizontal and vertical excitations are considered.