In mathematical modeling of geophysical fields in a real environment, a package of layers is often used as a model of the latter, since the primary occurrence of layers and formations is usually horizontal. In order to predict and prevent geophysical, as well as related technical disasters in the face of increasing technogenic environmental loads, there is an acute issue of developing models of physical and mechanical processes in geomaterials. The need to increase the probability of prognostic estimates for the occurrence of catastrophic situations requires more precise calculations concerning the dynamic behavior of extended objects with complex structure and physical and mechanical properties. In the paper we consider the plane problem of vibration for a half-space with coating, modeled by an elastic layer, in the presence of a liquid layer between them. The amplitude values of the displacements for elastic media are described by the steady-state Lame equations, the liquid velocity potential satisfies the Helmholtz equation. Solutions of boundary value problems describing the behavior of a hydroelastic layered medium are built on the basis of an integral approach. The heterogeneity of the foundation structure necessitates the decomposition of the model. We obtain the integral characteristics of normal pressures at the boundaries of the liquid layer by solving the problems for each of the three media, taking into account the layer conjugation conditions. The results of model calculations for normal pressures in the media interface are presented. The considered model can be used in studying the features of the interaction between vibration sources and the geophysical environment, modeled by a multilayer foundation containing liquid interlayers.

В работе рассматривается плоская задача о вибрации полупространства с покрытием, моделируемым упругим слоем, при наличии между ними жидкой прослойки. Решения краевых задач, описывающих поведение гидроупругой слоистой среды, строятся на основе интегрального подхода. Неоднородность строения основания обуславливает необходимость декомпозиции модели. После решения задач для трех сред с учетом условий сопряжения слоев получены интегральные характеристики нормальных давлений на границах жидкой прослойки. Приведены результаты модельных расчетов для нормальных давлений в области раздела сред. Рассмотренная модель может быть использована при исследовании особенностей взаимодействия вибрационных источников с геофизической средой, моделируемой многослойным основанием, содержащем заглубленные жидкие слои.