Abstract
The dynamic response of a one-dimensional problem for a thermoelastic rod with finite length is investigated in the context of the fractional order theory of thermoelasticity in the present work. The rod is fixed at both ends and subjected to a moving heat source. The fractional order thermoelastic coupled governing equations for the rod are formulated. Laplace transform as well as its numerical inversion is applied to solving the governing equations. The variations of the considered temperature, displacement, and stress in the rod are obtained and demonstrated graphically. The effects of time, velocity of the moving heat source, and fractional order parameter on the distributions of the considered variables are of concern and discussed in detail.
Highlights
The classical coupled thermoelasticity proposed by Biot [1] predicts an infinite speed for heat propagating in elastic media, which is physically impossible
We investigate the dynamic problem of a thermoelastic rod subjected to a moving heat source in the context of fractional order theory of thermoelasticity
Three time instants, t = 1.0, t = 1.5, and t = 2.0, are considered, while the heat source velocity and the fractional order parameter remain constant as υ = 2.0 and α = 0.25, respectively
Summary
The classical coupled thermoelasticity proposed by Biot [1] predicts an infinite speed for heat propagating in elastic media, which is physically impossible. There exist many materials and physical situations such as low-temperature regimes, amorphous media, colloids, glassy and porous materials, man-made and biological materials/polymers, and transient loading, where the classical coupled thermoelasticity and the generalized thermoelastic theories fail In such cases, it may be necessary to introduce time-fractional derivatives into thermoelasticity. 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. The variations of the considered variables are obtained and illustrated graphically
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