Investigation on the dynamic responses of a generalized thermoelastic problem with variable properties and nonlocal effect

Abstract

To explore the dynamic responses of generalized thermoelastic problems with nonlocal effect in microtemporal scale, a finite length thermoelastic rod subjected to a moving heat source is modeled and investigated in generalized thermoelasticity. The rod is fixed at both ends and its material properties are temperature-dependent. The corresponding governing equations are first given and then reduced into one-dimensional ones with temperature-dependent properties assumed to be functions of reference temperature. Subsequently, the equations after normalization are solved together with the initial conditions and the boundary conditions by means of Laplace transform and its numerical inversion. The distributions of the nondimensional temperature, displacement, and stress are obtained and illustrated graphically. In calculation, the effects of the velocity of the heat source, the temperature-dependent properties and the nonlocal parameter on the distributions of the considered variables are emphatically examined and discussed in detail. The results show that the velocity of the heat source and the variable properties markedly influence the variations of the considered variables, while the nonlocal parameter barely influences the variations of the nondimensional temperature, slightly influences the variations of the peak value of the nondimensional displacement and significantly influences the variations of the peak value of the nondimensional stress.