External boundary value problems of steady vibrations in the theory of rigid bodies with a double porosity structure

This paper concerns with the linear 3D theory of rigid solids with a double porosity structure. Basic external boundary value problems (BVPs) of steady vibrations are formulated. The uniqueness and existence theorems for regular (classical) solutions of these BVPs are established. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Steady vibrations problem in the theory of viscoelasticity for Kelvin-Voigt materials with voids

In this paper the linear theory of viscoelasticity for Kelvin-Voigt materials with voids is considered. The uniqueness and existence theorems for internal boundary value problem (BVP) of steady vibrations are proved by means of the potential method (boundary integral method) and the theory of singular integral equations. The application of this method to the 3D BVP of the considered theory reduces this problem to 2D singular integral equation. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Explicit solution of the boundary value problem of the theory of thermoelasticity with microtemperatures for elastic circle

In this paper we solve explicitly, by means of absolutely and uniformly convergent series, the 2D boundary value problem (BVP) of statics of the linear theory of thermoelasticity with microtemperatures for an elastic circle. The uniqueness theorem of the internal BVP is proved. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Explicit solution of the boundary value problems of the theory of elasticity for solids with double porosity

In this paper the Aifantis' theory of elasticity for solids with double porosity is considered and the 2D boundary value problem (BVP) of static is investigated. The uniqueness theorem of the internal BVP is proved. The explicit solution the BVP is constructed in the form of absolutely and uniform convergent series for a circle. The numerical solution of the BVP for a circle is obtained. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On representations of a general solution in the theory of micropolar thermoelasticity without energy dissipation

In the present paper, the linear theory of micropolar thermoelasticity without energy dissipation is considered. This work is organized as follows: Section 2 is devoted to basic equations for micropolar thermoelastic materials, supposed to be isotropic and homogeneous, and to assumptions on constitutive constants. In Section 3, some theorems related to representations of a general solution are studied. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 10, pp. 1391–1398, October, 2007.     

Boundary value problems of the theory of heat propagation in a binary mixture

In this paper we study the problems of heat propagation in a binary mixture. The fundamental solution of system of equations of steady vibrations is constructed in terms of elementary functions. The uniqueness and existence theorems of classical solution of the interior and exterior boundary value problems by means of the boundary integral method are proved. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Plane waves and vibrations in the theory of micropolar thermoelasticity for materials with voids

The present paper concerns with the linear theory of micropolar thermoelasticity for materials with voids. Some basic properties of wave numbers of the longitudinal and transverse plane harmonic waves are treated. The existence theorems of non-trivial solutions and eigenfrequencies of the interior homogeneous boundary value problems of steady vibrations are proved. The connection between plane harmonic waves and eigenfrequencies of the aforementioned problems is established.     

Fundamental Solution of the System of Equations of Steady Oscillations in the Theory of Fluid-Saturated Porous Media

In the present paper the linear theory of the liquid-saturated porous medium consisting of a microscopically incompressible solid skeleton containing microscopically incompressible liquid is considered. The fundamental solution of the system of linear coupled partial differential equations of the steady oscillations of the porous solids is constructed in terms of elementary functions and some basic properties are established.