S. M. Abo-Dahab

Effects of voids and rotation on P wave in a thermoelastic half-space under Green–Naghdi theory

In this paper, the problem of wave propagation in a thermoelastic solid half-space with voids and rotation is considered in context of the Green–Naghdi theory of thermoelasticity. The basic governing equations for an isotropic and homogeneous thermoelastic half-space are formulated and solved analytically. The solution of the governing equations indicates the existence of four coupled plane waves, namely P1, P2, P3 and P4, in the medium. The boundary conditions at the thermally insulated stress-free surface are satisfied by the particular solutions in the half-space to obtain analytically the expressions for reflection coefficients of various reflected waves. A numerical example is chosen to study the velocities and reflection coefficients numerically to observe the effects of voids and rotation.

On a Problem of Nonstationary 2D Motion of Micropolar Fluid in the Half-plane Subjected to a Uniform Magnetic Field when Normal Stresses and Tangential Velocities are Given on the Boundary

Abstract In this paper, an attempt is made to obtain the effect of a uniform magnetic field on the solution of non-stationary motion of micropolar fluid in the half-plane when the normal stresses and tangential velocities are given on the boundary. The Laplace-Fourier transform technique is used to point out the solution by quadratures. Numerical results of the physical quantities such as tangential and normal velocities, pressure, microrotation, stresses and momentums included the influence of a uniform magnetic field are obtained and displayed graphically. The problem could be met in the study of the vibrations of a memberance or a plane contacting with the micropolar fluid.