The effect of fractional parameter on a perfect conducting elastic half-space in generalized magneto-thermoelasticity

Abstract

Recently, Sherief et al. (Int. J. Solids Struct. 47:269–275, 2010) proposed a model in generalized thermoelasticity based on the fractional order time derivatives. The propagation of electro-magneto-thermoelastic disturbances in a perfectly conducting elastic half-space is investigated in the context of the above fractional order theory of generalized thermoelasticity. There acts an initial magnetic field parallel to the plane boundary of the half-space. Normal mode analysis together with the eigenvalue approach technique is used to solve the resulting non-dimensional coupled governing equations of the problem. The obtained solution is then applied to two specific problems for the half-space, whose boundary is subjected to (i) thermally isolated surfaces subjected to time-dependent compression and (ii) a time-dependent thermal shock and zero stress. The effects of fractional parameter and magnetic field on the variations of different field quantities inside the half-space are analyzed graphically.