Thermoelastic responses of a finite rod due to nonlocal heat conduction

Based upon the Lord and Shulman theory of thermoelasticity, the new governing equations of thermoelasticity with nonlocal heat conduction are formulated. The above model is then employed to study the transient responses of a thermoelastic rod of finite length when subjected to a moving heat source. Both ends of the rod are assumed to be fixed and thermally insulated. The Laplace transform technique is used to obtain the analytical solutions for the field variables such as temperature, displacement, and stress. The inverse Laplace transform based on the Zakian algorithm is numerically implemented to obtain the solutions of the above physical variables in the space–time domain. Specific attention is paid to the study of the effect of the thermal nonlocal parameter on the distributions of the field variables and the speed of the moving heat source.