Computer simulating the forced vibrations of structure elements interacting with liquid under harmonic, impulse and seismic excitations

Abstract

The method for simulating forced vibrations of structure elements, which interact with water medium during service is developed. Harmonic, impulse and seismic loadings are accounted for. It is assumed that the fluid surrounding the structure element is an ideal and incompressible one, and its movement caused by the vibrations of the element in question is vortex-free. Therefore the velocity potential that satisfies the Laplace equation exists. To determine the fluid pressure on the surfaces contacting with the liquid the Cauchy-Lagrange integral is used. The velocity potential is determined by solving the Neumann boundary value problem for the Laplace equation on an open surface. The potential of the double layer is used as an integral representation. This potential satisfies the Laplace equation and the conditions for vanishing velocity at infinity. The non-penetration condition leads to the necessity of solving the hypersingular integral equation for the pressure drop. To solve the boundary value problem of hydroelasticity the method of given forms is applied. The unknown displacements and potential are represented as series with unknown coefficients. The basic functions in these series are the modes of vibrations of the element without liquid. The frequencies of the structure element vibrations in fluid are evaluated taking the added masses into account. For simulating forced vibrations the system of second order differential equations relatively to the unknown time-dependent coefficients is obtained. The vibrations of a rigidly clamped square plate are examined as an example. The behavior of the maximum stress intensity is analyzed in dependence with the loading parameters. The estimations for critical values of load parameters are provided.