A Problem on Elastic Half Space Under Fractional Order Theory of Thermoelasticity

Abstract

The present work is concerned with the solution of a problem on fractional order theory of thermoelasticity for an elastic medium. We investigate the thermoelastic interactions inside the medium by employing the fractional order theory of thermoelasticity, recently advocated by Sherief et al. (Int. J. Solids Struct., 47, 269-275, 2010). State space approach together with the Laplace transform technique is used to obtain the general solution of the problem. The general solution is then applied to three specific problems on an elastic half space, whose boundary is subjected to (i) a thermal shock (i.e., a step input in temperature and zero stress), (ii) a normal load (i.e., a step input in stress and zero temperature change) and (iii) a ramp type increase in temperature and zero stress. To observe the variations of displacement, temperature and stress inside the half-space we compute the numerical values of the field variables for a particular material by utilizing a numerical method of Laplace inversion. The effects of fractional order parameter on the variations of different fields inside the medium are analyzed graphically.

Heating a thermoelastic half space with a surface absorption pulsed laser using fractional order theory of thermoelasticity

“…As a generalization to both coupled and generalized theories, Sherief et al (2010) formulated the fractional order theory of thermoelasticity. Using Sherief's model, the solution of a thermoelasticity problem was successfully obtained for a semi-infinite medium possessing three different boundary conditions by applying the state space approach and the Laplace transform (Kothari and Mukhopadhyay, 2011). Sherief and Abd El-Latief (2013) solved a one-dimensional thermal shock problem for a semi-infinite body whose thermal conductivity was variable.…”

Effect of Variable Properties and Moving Heat Source on Magnetothermoelastic Problem under Fractional Order Thermoelasticity

“…To obtain the parameters of ( = 1, 2, 3, 4) and ( = 1, 2, 3, 4), (32) and (38) are substituted into the equation of boundary conditions as follows:…”

“…Recently, a completely new fractional order generalized thermoelasticity theory was introduced by Sherief et al [31]. Based on this theory, Kothari and Mukhopadhyay [32] solved an elastic half-space problem via Laplace transform and state-space method. Sherief and Abd El-Latief [33] investigated a half-space problem with varying extent of thermal conductivity.…”

A One-Dimensional Thermoelastic Problem due to a Moving Heat Source under Fractional Order Theory of Thermoelasticity

“…Very recently, a completely new theory on fractional order generalized thermoelasticity has been introduced by Sherief et al [27]. By employing this theory, Kothari and Mukhopadhyay [28] solved an elastic half-space problem with Laplace transform and state-space method. Sherief and Abd El-Latief [29] investigated a halfspace problem with different thermal conductivity under the theory of fractional order.…”