Chapter 33 Study of Stability Matter Problem in Micropolar Generalised Thermoelastic

摘要

The theory of micropolar thermoelasticity has many applications. One form of the recent years concerning the problem of propagation of thermal waves at finite speed and the possibility of "second sound" effects established a new thermo mechanical theory of deformablemedia that uses a general entropy balance as postulated and the theory is illustrated in detail in the context of flowof heat in a rigid solid, with particular reference to the propagation of thermal waves at finite speed. Then theory of thermoelasticity for non-polar bodies, based on the new procedures, was discussed and employed the eigen value approach to study the effect of rotation and relaxation time in two dimensional problem of generalized thermoelasticity.Recently investigation shows the dynamic response of a homogeneous, isotropic, generalized thermoelastic half-space with voids subjected to normal, tangential force and thermal stress. In this paper we introduce the eigen value approach, following Laplace and Fourier transformation has been employed to find the general solution of the field equation in a micropolar generalized thermoelastic medium for plane strain problem. An application of an infinite space with an impulsive mechanical source has been taken to illustrate the utility of the approach. The integral transformation has been inverted by using a numerical inversion technique to get result in physical domain. The result in the form of normal displacement, normal force stress, tangential force stress, tangential couple stress and temperature field components have been obtained numerically and illustrated graphically. Special case of a thermoelastic solid has also been deduced.