Response Of Fractional Order Theories Of Thermoelasticity In a Micropolar Viscothermoelastic Solid

Abstract

The present work deals with the study of thermoelastic interaction in a micropolar viscoelastic solid usingfractional order theories of thermoelasticityderived by Sherief et.al (2010),Ezzat (2010)and Youssef (2010).A mathematical model has been developed to find a common solution corresponding to different theories under consideration. Laplace and Fourier transform techniques are used to find the general solution in the transform domain. The general solution then applied to a specific problem of a micropolar viscothermoelastic half space, which is subjected to a ramp-type increase in temperature with zero stress, and ramp-type increase in normal load with zero temperature change physical field quantities(displacement,stresses,temperature field) are obtained in transformed domain.These quantities are recovered in the physical domain by using numerical inversion technique and displayed in the form of graphs. Some particular case of interest are also deduced from the present study