Nonlinear Stability of Thermoelastic Sliding Contact

[+] Author and Article Information
Jason D. Miller, D. Dane Quinn

Department of Mechanical Engineering,  The University of Akron, Akron, OH 44325-3903

J. Appl. Mech 74(3), 595-598 (Oct 05, 2005) (4 pages) doi:10.1115/1.2423034 History: Received November 19, 2004; Revised October 05, 2005

A model for sliding contact of a thermoelastic rod is considered and is subjected to a multiple scales analysis to uncover its nonlinear behavior near a neutrally stable state. The analysis reveals a combination of the contact resistance and frictional intensity that describes the generic unfolding of this critical state and its associated bifurcations. In particular, the system can describe how two equilibria coalesce in a saddle-node bifurcation and generalizes stability criteria that have been presented previously in the literature for this model. Moreover, this analysis describes the role of the initial deformation of the rod on its long-term dynamical behavior.

Copyright © 2007 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Bifurcation diagram (β1∕(2β2)=1.00, β0∕β2=0.25, β2>0). Stable equilibrium solutions are denoted by the solid line, while the dashed branch is unstable. The arrows denote the general evolution of initial conditions and in the shaded region initial conditions grow unbounded. The location of the saddle-node bifurcation is marked with the open circle. Finally, the response shown in Fig. 2 occurs for the dotted line at γ3=3.00.

Grahic Jump Location
Figure 2

Solutions for λ1,2={1.5,0.5} (β0=0.25, β1=2.00, β2=1, γ3=3.00). The equilibrium solutions are shown as thick lines (solid—stable, dashed—unstable).



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