Exponential decay in one-dimensional type III thermoelasticity with voids (original) (raw)

On the spatial behavior in two-temperature generalized thermoelastic theories

Zeitschrift für angewandte Mathematik und Physik

This paper investigates the spatial behavior of the solutions of two generalized thermoelastic theories with two temperatures. To be more precise, we focus on the Green-Lindsay theory with two temperatures and the Lord-Shulman theory with two temperatures. We prove that a Phragmén-Lindelöf alternative of exponential type can be obtained in both cases. We also describe how to obtain a bound on the amplitude term by means of the boundary conditions for the Green-Lindsay theory with two temperatures.

A theory of thermoelastic materials with voids

Acta Mechanica, 1986

A linear theory of thermoelastic materials with voids is considered. First, some general theorems (uniqueness, reciprocal and variational theorems) are established. Then, the acceleration waves and some problems of equilibrium are studied.

On the harmonic vibrations in linear theory of thermoelasticity of type III

Mechanics Research Communications, 2011

In the present paper we consider the linear theory of thermoelasticity of type III as developed by Naghdi (1992, 1995). Within the context of the harmonic vibrations, we establish some estimates describing the spatial behavior of the corresponding amplitudes, provided the frequency is lower than a certain critical value. It is shown that such critical frequency is influenced only by the mechanical effects. Extension of results to the strongly elliptic thermoelastic materials is also discussed.

On the Nonlinear Theory of Nonsimple Thermoelastic Materials with Voids

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1993

On the Nonlinear Theory of Nonsimple Thermoelastic Materials with Voids E.Y wird eine nichtlineare Theorie des nichteinfachen, thermoelastischen Materials mit Poren aufgestellt. Die kontinuierliche Ahlzungigkeit con Anfangszustand und Erganzungstermen des glatten therrnodynamischen Prozesses wird untersuclzt. A nonlinear theory of nonsimple thermoelastic materials with voids is established. The continuous &pendenre upon initial state and supply terms of smooth thermodynamic processes is studied.

On uniqueness and analyticity in thermoviscoelastic solids with voids

Journal of Applied Analysis and Computation, 2011

In this paper we consider the most general system proposed to describe the thermoviscoelasticity with voids. We study two qualitative properties of the solutions of this theory. First, we obtain a uniqueness result when we do not assume any sign to the internal energy. Second we extend some previous results and prove the analyticity of the solutions. The impossibility of localization in time of the solutions is a consequence. Last result we present corresponds to the analyticity of solutions in case that the dissipation is not very strong, but with suitable coupling terms.

Potential method in the theory of thermoelasticity for materials with triple voids

Archives of Mechanics, 2019

In the present paper the linear theory of thermoelasticity for isotropic and homogeneous solids with macro-, meso-and microporosity is considered. In this theory the independent variables are the displacement vector field, the changes of the volume fractions of pore networks and the variation of temperature. The fundamental solution of the system of steady vibrations equations is constructed explicitly by means of elementary functions. The basic internal and external boundary value problems (BVPs) are formulated and the uniqueness theorems of these problems are proved. The basic properties of the surface (single-layer and double-layer) and volume potentials are established and finally, the existence theorems for regular (classical) solutions of the internal and external BVPs of steady vibrations are proved by using the potential method (boundary integral equation method) and the theory of singular integral equations.

On a Theory of Thermoviscoelastic Materials with Voids

Journal of Elasticity, 2011

In this paper we extend the theory of elastic materials with voids to the case when the time derivative of the strain tensor and the time derivative of the gradient of the volume fraction are included in the set of independent constitutive variables. First, the basic equations of the nonlinear theory of thermoviscoelastic materials with voids are established. Then, the linearized version of the theory is derived. We establish a uniqueness result and the continuous dependence of solution upon the initial data and supply terms. A solution of the field equations is also presented.

Plane harmonic waves in the theory of thermoviscoelastic materials with voids

Journal of Thermal Stresses, 2016

In this article we analyze the behavior of plane harmonic waves in the entire space lled by a linear thermoviscoelastic material with voids. We take into account the e ect of the thermal and viscous dissipation energies upon the corresponding waves and, consequently, we study the damped in time wave solutions. There are ve basic waves in an isotropic and homogeneous thermoviscoelastic porous space. Two of them are shear waves, while the remaining three are dilatational waves. The shear waves are uncoupled, damped in time with decay rate depending only on the viscosity coe cients. The three dilatational waves are coupled and consist of a predominantly dilatational damped wave of Kelvin-Voigt viscoelasticity, other is predominantly a wave carrying a change in the void volume fraction and the third takes the form of a standing thermal wave whose amplitude decays exponentially with time. The explicit form of the dispersion equation is obtained in terms of the wave speed and the thermoviscoelastic homogeneous pro le. Furthermore, we use numerical methods and computations to solve the secular equation for some special classes of thermoviscoelastic materials considered in literature.