Nonlinear stability, thermoelastic contact, and the Barber condition

The behavior of a one-dimensional thermoelastic rod is modeled and analyzed . The rod is held fixed at constant temperature at one end, while at the ot her end it is free to separate from or male contact with a rigid wall. At t his free end we impose a pressure and a gap-dependent thermal boundary cond ition. Thus condition, known as the Barber condition, couples the thermal a nd elastic problems. Such systems have previously been shown to undergo a b ifurcation from a unique linearly stable steady-state solution to multiple steady-state solutions with alternating stability. Here, the system is stud ied using the asymptotic matching techniques of boundary layer theory to de rive short-time, long-time and uniform expansions. In this manner the analy sis is extended into the nonlinear regime and dynamic information about the history dependence and temporal evolution of the solution is obtained.