SOLITON-LIKE SOLUTIONS IN A NONLINEAR DYNAMIC COUPLED THERMOELASTICITY
Titel:
SOLITON-LIKE SOLUTIONS IN A NONLINEAR DYNAMIC COUPLED THERMOELASTICITY
Auteur:
Ignaczak, Jozef
Verschenen in:
Journal of thermal stresses
Paginering:
Jaargang 13 (1990) nr. 1 pagina's 73-98
Jaar:
1990
Inhoud:
This paper examines propagation of soliton-like waves in a nonlinear homogeneous isotropic thermoelastic solid in which both the free energy and the heat flux vector depend not only on the absolute temperature and strain tensor but also on an “elastic” heat flow that satisfies an evolution equation. This equation, together with the equation of motion and the energy conservation law, leads to a nonlinear coupled system of partial differential equations from which the temperature, strain, and heat flux fields are to be found. For a one-dimensional case the system admits two closed-form solutions of the soliton type corresponding to two one-way waves propagating with velocities V1, and V2, (0 < V1, < V2) the velocities satisfy a biquadratic equation similar to that for the longitudinal waves of linear thermoelasticity with finite wave speeds. Between the ith temperature soliton Ti, = Ti, (si = x — Vi-,t; |x | < +∞, t it = 0, i = 1, 2) and the ith strain soliton u˙i(Si ), a simple relation is established. A simple relation is also obtained between Ti(Si) and the ith heat flux soliton qi,(Si) The derived equations imply that the nonlinear thermoelastic model admits large temperature deviations from a unit temperature and small strains if the velocity of the slower(faster) soliton belongs to a left-hand (right-hand) neighborhood of a unit velocity, and that a contribution of elastic heat flow to total heat flux for the ith soliton is proportional to √i 1. In particular, for the slower soliton, the contribution is significant if Vi, is small. Moreover, high and low temperature wave fronts for the slower soliton as well as a low temperature wave front for the faster soliton are revealed.
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