A GENERALIZED THERMOELASTIC PROBLEM WITH NONLOCAL EFFECT AND MEMORY- DEPENDENT DERIVATIVE

The existing generalized thermoelastic theory is mainly applicable to obtain the dynamic responses of the problems in which the time scale is extremely short while the spatial scale is still macro-scale. Nevertheless, when the characteristic length scale of elastic body is also of micro-scale, the dynamic responses of the elastic body will take on intense size-dependent effect, and the existing generalized thermoelastic theory will be no longer suitable for such problems. In present work, based upon the generalized thermoelasticity with nonlocal effect and memory-dependent derivative, the dynamic response of a finite thermoelastic rod fixed at both ends and subjected to a moving heat source is investigated. The corresponding governing equations of the problem are formulated and the initial conditions as well as the boundary conditions are specified. Then, the governing equations are solved by means of Laplace transform and its numerical inversion. In calculation, first, the influence of the time-delay factor on the distributions of the considered physical quantity was examined. Then, the influence of the time-delay factor on the distributions of the considered variables under two kinds of kernel functions (i.e. normalized form and unmodified form) was compared. Last, the influence of the nonlocal factor on the dimensionless temperature, displacement and stress is considered and illustrated graphically. The results show that: with the increase of the time-delay factor, the heat wave propagation velocity becomes smaller, the peak values of the physical quantities become larger, and the influence of the time delay factor on the considered variables is more significant in the case with the kernel function modified by normalized condition than that with unmodified kernel function; The non-local parameter barely affects the distribution of the dimensionless temperature, slightly affects the distribution of the dimensionless displacement, while markedly affects the peak values of the dimensionless stress.