This paper studies the spatial behaviour of the amplitude of a harmonic vibration in a rectangular plate of Mindlin type, made of a homogeneous and isotropic elastic material with voids. Provided the frequency of vibration is lower than the critical value, some appropriate measures are introduced relating the amplitude of resulting harmonic vibration, and the corresponding first-order differential inequalities are established under mild conditions

In the present paper, we investigate a model for propagating progressive waves associated with the voids within the framework of a linear theory of porous media. Owing to the use of lighter materials in modern buildings and noise concerns in the environment, such models for progressive waves are of much interest to the building industry. The analysis of such waves is also of interest in acoustic microscopy where the identification of material defects

This paper is devoted to the study of a binary homogeneous mixture of an isotropic micropolar linear elastic solid with an incompressible micropolar viscous fluid. Assuming that the internal energy of the solid and the dissipation energy are positive definite forms, some uniqueness and continuous data dependence results are presented. Also, some estimates which describe the time behaviour of solution are established, provided the above two energies

The aim of this paper is to study the asymptotic partition of the energy associated with the solution of the initial-boundary value problem who describes the behavior of binary homogeneous micropolar mixtures of an isotropic micropolar elastic solid with an incompressible micropolar viscous fluid. Some Lagrange-Brun identities are established. Using the Cesáro means of various parts of total energy, the relations that describe the asymptotic behavior

The purpose of this research is to study the Saint-Venant's problem for right cylinders with general cross-section made of inhomogeneous anisotropic elastic materials with voids. We reformulate the quasi-static equilibrium equations with the axial variable playing the role of a parameter. Two classes of semi-inverse solutions to Saint-Venant's problem are described in terms of five generalized plane strain problems. These classes are used in order

In this paper we study the existence and uniqueness of solutions for the initial-boundary value problem of a micropolar binary mixture.We use some results of the semigroup theory of linear operators to obtain an existence and uniqueness theorem for the initial value problem with homogeneous Dirichlet boundary conditions. Continuous dependence of the solutions upon the initial data and supply terms is also established.

The present paper studies the uniqueness and continuous data dependence of solutions of the initial-boundary value problem associated with the micropolar mixture linear theory of porous media. For a binary homogeneous mixture of an isotropic micropolar elastic solid with an incompressible micropolar viscous fluid, an uniqueness result is established. Then we deduce some estimates for describing the continuous dependence of solution with respect to

This paper studies the spatial behaviour of the steady-state vibrations in a right elastic cylinder, under mild conditions upon the elastic coefficients. In fact, we establish some exponential decay estimates of Saint-Venant type for two cross-sectional area measures associated with the amplitude of the steady-state vibrations, provided that the elasticity tensor is assumed to be strongly elliptic and the prescribed frequency is lower than a certain