Учет трения в области контакта при колебаниях жесткого штампа на поверхности полуограниченной среды

Abstract

The dynamic contact problem of oscillation of a rigid punch on a semi-infinite viscoelastic base is considered, moreover, friction in the contact area is taken into account. The base is provided with a microstructure wich is determinated in the framework of the micromechanics model. The problem is considered in a flat formulation for a steady-state oscillation regime. The base is modeled by a viscoelastic half-space. A rigid punch oscillates on the day surface of the elastic half-space. Normal and tangential stresses in the contact area are related by the Amonton-Coulomb law. Displacements satisfy the Lamaet equations. The connection of displacements and stresses is given by the generalized Hooke's law. The solution of this boundary value problem is constructed using the Fourier transform, which is applied to the Lamaet equations and boundary conditions. The base microstructure was taken into account in the framework of the micromechanics model. Mechanical characteristics corresponding to an equivalent elastic medium have been determined. The boundary-value problem is reduced to an integral equation of the first kind with a difference kernel. The numerical discretization of the integral equation is based on the collocation method. As a regularizer of the main part of the kernel, a function is used to isolate the logarithmic singularity, which coincides with it at infinity and has no singularities in the complex plane. As a result of discretization, the solution reduces to a finite system of equations with a quasi-diagonal matrix. The numerical analysis of the solution of the dynamic contact problem allowed us to draw the following conclusions. The change in contact stresses depending on the coefficient of friction in the contact region substantially depends on the oscillation frequency of the stamp. A significant effect on contact stresses is exerted by the coefficient of friction and the mechanical characteristics of the base material.