The paper considers the contact problem of vibration of a rigid punch with a plane base on a microneogeneous viscoelastic half-space when friction in the contact region is taken into account. The microheterogeneity of the medium is taken into account in the framework of the Biot-Frenkel multiphase medium model for porous-elastic fluid-saturated medium. The viscosity of the fluid filling the pores is taken into account and the skeleton is assumed to be viscoelastic. Rheological properties of the skeleton are taken into account in the framework of the concept of complex modules. The boundary value problem for the Biot medium is reduced to an integral equation of the first kind with a difference kernel with respect to normal contact pressures. The solution of the integral equation after regularization by feature extraction is realized numerically by the boundary element method. Numerical experiment has been carried out for the skeleton material, an epoxyphenolic resin modified with magnesium oxide, which contains cylinder oil in its pores. The viscoelastic skeleton is described within the framework of the standard viscoelastic body model with long modulus and instantaneous modulus and relaxation time. The dependence of contact stresses on the frequency oscillations has been investigated. On the basis of numerical experiments the range of frequencies has been established, for which it is shown that the account of friction in the contact area and viscosity of the matrix of heterogeneous medium has the greatest influence on the contact stresses.

Рассмотрена динамическая контактная задача о вибрации штампа с плоским основанием на микронеоднородном вязкоупругом полупространстве при учете трения в области контакта. Микронеоднородность среды учитывается в рамках модели Био-Френкеля для пористоупругой флюидонасыщенной среды, причем учитывается не только вязкость флюида, но и сам скелет предполагается вязкоупругим. Исследованы зависимости напряжений в области контакта от реологических свойств среды.