The behavior of a one-dimensional thermoelastic rod is modeled and analyzed. The rod is held fixed and at constant temperature at one end, while at the other end it is free to separate from or make contact with a rigid wall. At this free end we impose a pressure and gap-dependent thermal boundary condition. This condition, known as the Barber condition, couples the thermal and elastic problems. Such systems have previously been shown to undergo a bifurcation from a unique linearly stable steady-state solution to multiple steady-state solutions with alternating stability. Here, the system is studied using the asymptotic matching techniques of boundary layer theory to derive short-time, long-time, and uniform expansions. In this manner, the analysis is extended into the nonlinear regime and dynamic information about the history dependence and temporal evolution of the solution is obtained.
Nonlinear Stability, Thermoelastic Contact, and the Barber Condition
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, Sept. 24, 1999; final revision, June 26, 2000. Associate Editor: J. R. Barber. Discussion on the paper should be addressed to the Editor, Professor Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
Pelesko, J. A. (June 26, 2000). "Nonlinear Stability, Thermoelastic Contact, and the Barber Condition ." ASME. J. Appl. Mech. January 2001; 68(1): 28–33. https://doi.org/10.1115/1.1345699
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