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

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.

One-dimensional problem for infinitely long annular cylinder in the context of fractional order theory of thermoelasticity

“…R. Kumar and K. Singh studied interaction of fractional order theories in a micropolar thermoelastic solid due to ramp type heating in . T. He and Y. Guo studied a one‐dimensional thermoelastic problem due to a moving heat source under fractional order theory of thermoelasticity in . N. Sarkar and A. Lahiri studied the effect of fractional parameter on plane waves in a rotating elastic medium under fractional order thermoelasticity in .…”

Dynamic response of a one‐dimensional hexagonal quasicrystal rod in the framework of fractional‐order thermoelasticity

“…The other constants are taken as [36] $$$$\begin{equation} Q_{0}=10,\quad \tau _{0}=0.05,\quad L=10. \end{equation}$$$$…”

“…Substituting Equation (36) into Equations ( 31)-( 33), we can find the expressions of 𝑤 𝑧 and 𝜃 in Laplace domain, as follows:…”

Effect of Variable Thermal Conductivity on the Generalized Thermoelasticity Problems in a Fiber-Reinforced Anisotropic Half-Space

“…Normal mode analysis is applicable only for solving the steady state problem, whereas integral transformation and time-domain finite element method are suitable for solving dynamic problems. Integral transforms, such as Fourier and Laplace transforms, have been widely used for processing the related generalized thermoelastic problems [28][29][30]. In considering the effect of temperature-dependent variable conductivity in the fiber-reinforced generalized thermoelasticity problem, the governing equation has a nonlinear form.…”