D'ALEMBERT'S SOLUTION IN THERMOELASTICITY - IMPACT OF A ROD AGAINST A HEATED BARRIER: PART II. A CASE OF COUPLED STRAIN AND TEMPERATURE FIELDS

摘要

The problem of impact of a thermoelaslic rod against a heated rigid harrier is considered, in so doing lateral surfaces and free end of the rod are heat insulated, and free heat exchange between the rod and the rigid obstacle or ideal thermal contact occurs within contacting end. The rod's thermoelastic behavior is described by the Green-Naghdi theory of thermoelasticity. D'Alembert's method, which is based on the analytical solution of equations of the hyperbolic type describing the dynamic behavior of the thermoelastic rod, is used as the method of solution. This solution involves four arbitrary functions which are determined from the initial and boundary conditions and are piecewise constant functions. The procedure developed enables one to analyze the influence of thermoelastic parameters on the values to be found and to investigate numerically the longitudinal coordinate dependence of the desired functions at each fixed instant of the time beginning from the moment of the rod's collision with the barrier up to the moment of its rebound both without account for the stress and temperature fields coupling (in the companion paper, Part I) and in the case of coupling thermoelasticity (in this paper). As a numerical example, the impact of a thermoelastic rod against a heated barrier is considered with a small parameter of coupling between the strain and temperature fields. It has been shown that the presence of small coupling results in the generation of a new shock wave of small amplitude, namely: the reflected thermal wave from the incident elastic wave at the free rod's end. The rod's rebound may occur either at the moment of simultaneous arrival at the contact place of two reflected waves: elastic wave from the incident thermal wave and thermal wave from the incident elastic wave-or at the time when the reflected elastic-wave from the incident elastic wave reaches the contact point.