To the problem of vibrations of a limited volume of a liquid on an elastic foundation

Abstract

The paper presents a model of a hydro engineering structure under the influence of vibration loads, taking into account its interaction with an elastic foundation modeled by an isotropic layer or a half-space. The mathematical description of this model reduces to the formulation of a boundary-value problem for a system of partial differential equations, the solution of which leads to integral relations with respect to the unknown function of stresses, distributed over the area of contact between the surface object and the underlying foundation. Contact stresses are determined from the solution of the integral equation, the feature of which is the dependence of its kernel not only on the difference of the arguments, but also on their sum. Formulas for calculating the hydrodynamic pressure in the contact zone of the liquid and elastic media are obtained, as well as the velocity potential in the fluid and the displacements of the elastic foundation points. Analysis of the results of computational experiments made it possible to determine the dependencies of stresses in the media contact zone from the physical, geometric and frequency parameters of the problems under consideration for two models of an elastic foundation: an elastic half-space and an elastic layer with a fixed lower bound. The novelty of the conducted studies consists in analyzing the dynamic behavior of hydroelastic media based on solving integral equations, rather than using the average characteristics of contact stresses. Such approach will allow increasing the accuracy of the description of real processes and reliability of assessments of possible consequences of vibroseismic effects, which is especially important in regions where artificial and natural reservoirs and dams are near populated areas.