# thermoelasticity

## On the identification problem of the thermomechanical characteristics of the finite functionally graded cylinder

The problem of axisymmetric vibrations of a functionally graded finite hollow cylinder is considered. The ends of the cylinder are thermally insulated and are in a sliding fit. Zero temperature is maintained on the inner surface of the cylinder, free from stress, and a combined thermal and power load acts on the outer surface. The direct problem after applying the Laplace transform is solved based on the method of separation of variables.

## Covariant field equations and d-tensors of hyperbolic thermoelastic continuum with fine microstructure

A non-linear mathematical model of hyperbolic thermoelastic continuum with fine microstructure is proposed. The model is described in terms of 4-covariant field theoretical formalism. Fine microstructure is represented by d-tensors, playing role of extra field variables. A Lagrangian density for hyperbolic thermoelastic continuum with fine microstructure is given and the corresponding least action principle is formulated. 4-covariant field equations of hyperbolic thermoelasticity are obtained.

## The asymptotic separation of variables in thermoelastic problem for anisotropic layer with inhomogeneous boundary conditions

A method for resolving a thermoelasticity problem with inhomogeneous boundary conditions is presented. Boundary conditions represent uneven surface heating of the layer. An asymptotic procedure for separation of variables based on introduction of additional dimensional scales is used. With an additional assumption that the unevenness of the heating is small enough this procedure makes it possible to obtain the solution. The method is shown for periodic heating case. After the separation of variables the solution is obtained using Fourier series.

## Thermomechanical orthogonality in nonlinear type-III thermoelasticity (GNIII)

The present paper is devoted to formulations of constitutive equations for the non-linear Green–Naghdi type-III thermoelastic continuum consistent with the principle of thermodynamic (or thermomechanical) orthogonality.

## On precisely conserved quantities of coupled micropolar thermoelastic field

The paper is devoted to the 4-covariant formulation in fourdimensional space-time of dynamics of non-linear hyperbolic micropolar thermoelastic continuum. Theory ofmicropolar continuum are due to E. Cosserat and F. Cosserat and their study of 1909. The complement microdeformations and microrotations of an element are described by a non-rigid trihedron (the case of deformable micropolar directors).

## Oscillations of shallow shells at abrupt influence of thermal flow

On the basis of the closed integrals of the initial and boundary problems for incoherent thermoelastisity of shallow shells the quantitative analysis of influence of the geometrical parameters on the oscillations of constant rotation and cylindrical shells, which are conditioned by the thermal shock to outbound surface of shallow shell are carried out.

## Micropolar Thermoelastic Continuum Models with Constrained Microstructural Parameters

A new micropolar thermoelastic continuum model forrmulated by microstructural d-vectors and d-tensors of an arbitrary ranks is proposed. The microstructural vectorial and tensorial extra-field variables are restricted by holonomic or non-holonomic (differential) constraints. The study is carried out in the framework of the Lagrange field formalism as a 4covariant field theory.

## The Geometrical Irregular Plates under the Influence of the Quick Changed on the Time Coordinate Forces and Temperature Effects

On the basis of incoherent thermoelasticity, the dynamic behaviour of geometrically irregular plates under the influence of quick changed, on the time coordinate, forces and temperature effects on surfaces is considered. An approach allowing to obtain the analytical solution of the thermoelasticity dynamic problem for the plate under inhomogeneous boundary conditions at all four edges is suggested.

## Generalized Cross-Coupled Type-III Thermoelastic Waves Propagating via a Waveguide under Sidewall Heat Interchange

The paper is devoted to a study of cross-coupled type-III generalized thermoelastic waves propagation via a long cylindrical waveguide. The sidewall of the waveguide is assumed free from tractions and permeable to heat. The analysis is carried out in the framework of coupled generalized theory of GNIII- thermoelasticity consistent with the basic thermodynamic principles. The theory combines the both possible mechanisms of heat transfer: thermodiffusion and wave.

## Cross-Coupled Type-III Thermoelastic Waves of a Given Azimuthal Number in a Waveguide under Sidewall Heat Interchanging

The paper is devoted to a study of cross-coupled type-III generalized thermoelastic waves of a given azimuthal order propagating via a long cylindrical waveguide with circular cross-section. Sidewall of the waveguide is assumed free from tractions and permeable to heat. The study is carried out in the framework of coupled generalized theory of type-III thermoelasticity (GNIII) consistent with the fundamental principles of continuum thermomechanics. The type-III theory combines the both possible mechanisms of heat transfer: thermodiffusion and wave.