Free vibrations of anisotropic rectangular plate laying on a heterogeneous viscouselastic basis

The aim of the work. Free, transverse vibrations are considered heterogeneous along the three spatial coordinates of rectangular plates lying on an inhomogeneous viscoelastic base. It is assumed that the boundary conditions are homogeneous. A closed solution for the problem of free vibration of an inhomogeneous rectangular orthotropic plate based on an inhomogeneous viscoelastic foundation is developed in the article. Young's moduli and the density of the orthotropic plate continuously change with respect to three spatial coordinates, while the characteristics of a viscoelastic base change depending on the coordinates in the plane. Methods. The corresponding equation of motion is obtained using the classical theory of plates. The solution to the problem was constructed using the method of separation of variables and the Bubnov - Galerkin method. Results. Explicit formulas of the fundamental tone of the frequency of the transverse vibration of an anisotropic plate lying on an inhomogeneous viscoelastic base are determined. The influence of heterogeneity of orthotropic materials, viscosity inhomogeneities, inelastic and elastic substrates at dimensionless plate frequencies have been studied in detail.

3-D Model of the Periodic Structure Punch Sliding upon the Viscoelastic Base with Incompressible Fluid in the Contact Gap

In this paper the problem for a periodic structure punch sliding upon a viscoelastic layer bonded to a rigid half space is considered. The semi-analytical solution of the problem is developed. Influence of incompressible fluid in the gap between two bodies upon friction force, contact size and pressure distribution is analysed. The obtained model can be used in a number of practical applications, for example in accounting of automobile tire aquaplaning upon wet road surface.