Asymptotic behaviour in inhomogeneous linear thermoelasticity (original) (raw)

Asymptotic behaviour in n-dimensional thermoelasticity

Applied Mathematics Letters, 1997

We study the thermoelastic system and we prove that the divergence of the displacement vector field and the thermal difference decay exponentially as time goes to infinity. Moreover, we show that the decay cannot hold in general.

Asymptotic Behavior in Linear Thermoelasticity

Journal of Mathematical Analysis and Applications, 1999

This paper studies a linear thermoelastic material which exhibits a constitutive equation for heat flux with memory. An approximated theory of thermodynamics is developed for this model and a maximal pseudo free energy is explicitly constructed in the frequency domain. This thermodynamic potential is used to prove stability and domain of dependence results.

Reciprocal and variational principles in linear thermoelasticity without energy dissipation

Mechanics Research Communications, 2010

In the present paper we consider the equations which govern the behavior of an anisotropic and inhomogeneous centrosymmetric material within the framework of the linear theory of thermoelasticity without energy dissipation. We establish a reciprocal relation which is based on a characterization of the boundary-initial value problem in which the initial conditions are incorporated into the field equations. Further, a variational principle is presented too.

Spatial behavior for some non-standard problems in linear thermoelasticity without energy dissipation

Journal of Mathematical Analysis and Applications, 2010

In the present paper we consider a prismatic cylinder occupied by an anisotropic and homogeneous compressible linear thermoelastic material within the framework of the linear theory of thermoelasticity without energy dissipation. The cylinder is subject to zero body force and heat supply and zero lateral specific boundary conditions and the motion is induced by a time-dependent displacement and thermal displacement specified pointwise over the base. Further, the motion is constrained such that the displacement, thermal displacement, velocity and temperature variation at points in the cylinder and at a prescribed time are in given proportions to, but not identical with, their respective initial values. It is shown that certain integrals of the solution spatially evolve with respect to the axial variable. Conditions are derived that show the integrals exhibit alternative behavior and in particular for the semi-infinite cylinder that there is either at least exponential growth or at most exponential decay, provided the elasticity tensor is positive definite or strongly elliptic.

Asymptotic behaviour for a two-dimensional thermoelastic model

Mathematical Methods in the Applied Sciences, 2007

In this paper we study a thermoelastic material with an internal structure which binds the materials fibres to a quadratic behavior. Moreover a hereditary constitutive law for heat flux is supposed. We prove results of asymptotic stability and exponential decay for the evolution problem in two-dimensional space domain.

Thermoelasticity of initially stressed bodies, asymptotic equipartition of energies

International Journal of Engineering Science, 1998

In our study, we will extend the domain of influence in order to cover the thermoelasticity of initially stressed bodies with voids. In what follows, we prove that, for a finite time t > 0, the displacement field u i , the dipolar displacement field ϕ jk , the temperature θ and the change in volume fraction φ generate no disturbance outside a bounded domain B.