In this paper, we will give a global existence theorem in one-dimensional thermoelasticity with second sound in R. For this purpose, we first give the decay rates of the linearized equations with the help of Fourier sine and cosine transformation and the local existence theorem using theorems for quasi-linear symmetric hyperbolic systems. Then we establish some estimates in L, L and L∞ norms to...

First we prove an exponential decay result for solutions of the equations of linear, homogeneous, isotropic thermoelasticity in bounded regions in two or three space dimensions if the rotation of the displacement vanishes. As a consequence, we describe the decay in radially symmetrical situations, and in a cylinder in R3. Then we establish the global existence of solutions to the corresponding ...

A dynamical two dimensional problem of generalized thermoelasticity has been considered to examine the stresses in an isotropic elastic slab. Laplace transform for time variable and exponential Fourier transform for space variable has been applied in the basic equations to form a vector-matrix differential equation which is then solved by eigenvalue approach. Finally numerical computations of t...

In this paper, a continuum model based on the nonlocal elasticity theory is developed for vibration analysis of embedded orthotropic circular and elliptical micro/nano-plates. The nano-plate is bounded by a Pasternak foundation. Governing vibration equation of the nonlocal nano-plate is derived using Nonlocal Classical Plate Theory (NCPT). The weighted residual statement and the Galerkin method...

The forced vibration behaviors are examined for nonlocal strain gradient nanobeams with surface effects subjected to a moving harmonic load travelling with a constant velocity in terms of three beam models namely, the Euler-Bernoulli, Timoshenko and modified Timoshenko beam models. The modification for nonlocal strain gradient Timoshenko nanobeams is exerted to the constitutive equations by exc...

the nonlocal nonlinear buckling of a double layer graphene sheet (dlgs) covered by zinc oxide (zno) piezoelectric layers is investigated in this study. the surrounding circumstances of the system are considered as a pasternak foundation including spring constants and a shear layer. graphene sheets are subjected to longitudinal magnetic field and biaxial forces. on the other hand, the zno piezoe...

The importance of thermoelastic damping as a fundamental dissipation mechanism for small-scale mechanical resonators is evaluated in light of recent efforts to design high-Q micrometerand nanometer-scale electromechanical systems. The equations of linear thermoelasticity are used to give a simple derivation for thermoelastic damping of small flexural vibrations in thin beams. It is shown that Z...

We study a model for the semiconductor problem that consists of a system of dynamic thermoelasticity equations of displacement and semiconductor equations. This problem arises from the observation that semiconductor devices are too often cracked and broken because of the thermal stresses. Since the heat source generated by Joule heating is quadratic in the gradient of the electrical potential, ...

Flexural wave motion in an infinite transversely isotropic, thermoelastic plate in the context of conventional coupled thermoelasticity (CT), Lord-Shulman (LS) and Green-Lindsay (GL) theories of generalized thermoelasticity has been studied by asymptotic method. The asymptotic operator plate model for flexural motion in a transversely isotropic thermoelastic plate leads to fifth degree polynomi...

In this article we present the first results on domain decomposition methods for nonlocal operators. We present a nonlocal variational formulation for these operators and establish the well-posedness of associated boundary value problems, proving a nonlocal Poincaré inequality. To determine the conditioning of the discretized operator, we prove a spectral equivalence which leads to a mesh size ...