Shock Interaction in Thermoelastic Rods With Temperature and Strain Coupling

The problem of collinear collision of two thermoelastic rods with equal cross-section and rheological parameters but of different length and temperature is considered. Both rods move along the common longitudinal axes with different velocities, and one rod approaches the other. Their lateral surfaces and free ends are thermally insulated, and free thermal exchange is established via contacting ends. Thermoelastic behavior of the rods is described by the Green-Naghdy theory without energy dissipation, and D’Alembert solution is utilized as a method of solution. Since the coupling between the temperature and strain fields is assumed to be small, then the perturbation technique is used as well. The proposed procedure allows one to construct an analytical solution enabling to study the influence of thermoelastic parameters on the contact duration of two rods, as well as to obtain the stress, displacement velocity, temperature, and heat flow dependences of time and coordinate.