The dynamic contact problem of vibrations of a rigid punch on a semi-infinite heterogeneous foundation, consisting of a viscoelastic skeleton and a viscous fluid, is considered, taking into account friction in the contact area and phase interaction. The microstructure of the base is taken into account in the framework of the model of a heterogeneous medium, which is described by the Biot-Frenkel equations. The boundary value problem using the Fourier transform is reduced to an integral equation of the first kind with a difference kernel. After regularization the integral equation by explicitly identifying the singularity of its kernel, the solution is constructed approximately, while the numerical discretization of the contact area is carried out on the basis of the boundary element method. Approximate solutions are constructed that describe contact pressures and tangential displacements under the punch. The calculations were carried out for an oil-filled composite based on aromatic polyamide phenylone containing an aluminosilicate nanosized additive bentonite. The dependences of the propagation of surface waves with an increase in the viscosity and permeability of the base, the influence on the contact stresses of the oscillation frequency, porosity and permeability of a heterogeneous medium, and fluid viscosity are investigated. At low values, an increase in viscosity and a decrease in the permeability coefficient of the composite reduces the asymmetry of the distribution of contact stresses, and causes the maximum stress in the contact area to move during the oscillation period. At higher frequencies and higher viscosity, the effect of stress stabilization under the punch far from its edges is observed.

Рассмотрена динамическая контактная задача о колебаниях жесткого штампа на полуограниченном гетерогенном основании при учете трения в области контакта и взаимодействия фаз. Микроструктура основания учтена в рамках модели Био-Френкеля. Краевая задача с помощью преобразования Фурье сведена к интегральному уравнению первого рода, численная дискретизация которого осуществлена на основе метода граничных элементов. Исследовано влияние на контактные напряжения частоты колебаний, вязкости флюида и проницаемости гетерогенной среды.