Volume 240, Nº 2 (2019)

We study steady-state axisymmetric vibrations of finite-length piezoceramic cylinders subjected to electric loading. A key system of equations is constructed as result of the reduction of the system of equations of electroelasticity in a cylindrical coordinate system to a system of Hamilton-type equations or by using the conditions of stationarity of the functional of Hamilton–Ostrogradskii principle. In the first case, the transition to ordinary differential equations is performed by using finite-difference expressions. In the second case, it is necessary to use spline approximations of the first-order. For the solution of the obtained boundary-value problems, we apply the method of discrete orthogonalization. The results obtained by using the indicated methods are compared. The dependence of vibrations on the frequency of loading is analyzed for a radially polarized cylinder. The resonance frequencies are determined.

We model the frictionless contact between an elastic body and a rigid base with periodically placed quasielliptic grooves in the case where an incompressible liquid wetting the surfaces of the bodies is present near the edges of interface gaps. The middle parts of the gaps are filled with a gas under a constant pressure. Due to the surface tension of the liquid, a pressure drop described by the Laplace equation is formed in the liquid and in the gas. The posed contact problem for the elastic half space is reduced to a singular integral equation with Hilbert kernel for the derivative of the height of gaps and to a transcendental equation for the width of the area filled with gas. We analyze the dependences of the width of an area filled with gas, pressure drop, shape of the gaps, and the contact approach of the bodies on the applied load, volume of the liquid, and its surface tension.

We solve a contact problem of indentation of a punch into an elastic half space with regard for the friction and in the presence of the zones of adhesion, sliding, and separation. The applied approach is based on the statement of the problem in the form of the inverse problem in which the Coulomb law of friction is used as an additional condition in the regions with friction. In the formulation of the inverse problem, we take into account the presence of the zones of adhesion whose sizes are unknown. The correctness of the solution of the inverse problem is analyzed. The proposed approach, in combination with the procedure of discretization, enables us to determine the zones of microsliding alternating with the zones of adhesion and separation.

We propose a procedure for the construction of an equation of moisture transfer in soils with regard for the action of thermal and chemical factors. This procedure is based on the formulation of the equation of continuity containing the time derivative of a composite function for the liquid phase of a porous medium. As a result, the coefficients in the equation of moisture transfer depend on the variations of temperature, the concentrations of chemical substances in liquid and solid phases, and porosity as functions of time and contain the derivatives of density of the pore liquid and porosity as functions of temperature and the concentrations of chemical substances. The dependences of the parameters of the soil phase (density, coefficients of moisture transfer, diffusion coefficient of soil moisture, porosity, etc.) on the indicated factors are analyzed.