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TECHNICAL PAPERS

Nonlinear Stability, Thermoelastic Contact, and the Barber Condition

[+] Author and Article Information
J. A. Pelesko

School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160

J. Appl. Mech 68(1), 28-33 (Jun 26, 2000) (6 pages) doi:10.1115/1.1345699 History: Received September 24, 1999; Revised June 26, 2000
Copyright © 2001 by ASME
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References

Barber,  J. R., 1978, “Contact Problems Involving a Cooled Punch,” J. Elast., 8, pp. 409–423.
Barber,  J. R., Dundurs,  J., and Comninou,  M., 1980, “Stability Considerations in Thermoelastic Contact,” ASME J. Appl. Mech., 47, pp. 871–874.
Panek,  C., 1980, “A Thermomechanical Example of Auto-Oscillation,” ASME J. Appl. Mech., 47, pp. 875–878.
Olesiak,  Z. S., and Pyryev,  Y. A., 1996, “Transient Response in a One-Dimensional Model of Thermoelastic Contact,” ASME J. Appl. Mech., 63, pp. 575–581.
Barber,  J. R., 1981, “Stability of Thermoelastic Contact for the Aldo Model,” ASME J. Appl. Mech., 48, pp. 555–558.
Zhang,  R., and Barber,  J. R., 1990, “Effect of Material Properties on the Stability of Static Thermoelastic Contact,” ASME J. Appl. Mech., 57, pp. 365–369.
Yeo,  T., and Barber,  J. R., 1995, “Stability of a Semi-Infinite Strip in Thermoelastic Contact With a Rigid Wall,” Int. J. Solids Struct., 32, pp. 553–567.
Li,  C., and Barber,  J. R., 1997, “Stability of Thermoelastic Contact of Two Layers of Dissimilar Materials,” J. Therm. Stresses, 20, pp. 169–184.
Pelesko,  J. A., 1999, “Nonlinear Stability Considerations in Thermoelastic Contact,” ASME J. Appl. Mech., 66, pp. 109–116.
Friedman, B., 1990, Principles and Techniques of Applied Mathematics, Dover, New York.
Segel, L. A., 1966, “Nonlinear Hydrodynamic Stability Theory and Its Application to Thermal Convection and Curved Flows,” Non Equilibrium Thermodynamics: Variational Techniques and Stability, University of Chicago Press, Chicago, IL.
Kriegsmann,  G. A., and Wagner,  B. A., 1995, “Microwave Heating of Carbon-Coated Ceramic Fibers: A Mathematical Model,” IMA J. Appl. Math., 55, pp. 243–255.

Figures

Grahic Jump Location
Sketch of the model geometry
Grahic Jump Location
A typical contact resistance function
Grahic Jump Location
Geometric solution of the steady-state problem
Grahic Jump Location
Bifurcation diagram showing the constant in the steady solution as a function of the bifurcation parameter, δ
Grahic Jump Location
Behavior of solutions to the amplitude equation, which governs A(τ)

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