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TECHNICAL PAPERS

Vibration and Stability of Frictional Sliding of Two Elastic Bodies With a Wavy Contact Interface

[+] Author and Article Information
Mikhail Nosonovsky

Department of Mechanical Engineering, Ohio State University, Columbus, OH 43202

George G. Adams

Department of Mechanical Engineering, Northeastern University, Boston, MA 02115e-mail: adams@coe.neu.edu

J. Appl. Mech 71(2), 154-161 (May 05, 2004) (8 pages) doi:10.1115/1.1653684 History: Received December 02, 2001; Revised September 19, 2003; Online May 05, 2004
Copyright © 2004 by ASME
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References

Adams,  G. G., 1995, “Self-Excited Oscillations of Two Elastic Half-Spaces Sliding With a Constant Coefficient of Friction,” ASME J. Appl. Mech., 62, pp. 867–872.
Renardy,  M., 1992, “Ill-Posedness at the Boundary for Elastic Solids Sliding Under Coulomb Friction,” J. Elast., 27, pp. 281–287.
Simões,  F. M. F., and Martins,  J. A. C., 1998, “Instability and Ill-Posedness of Some Frictional Problems,” Int. J. Eng. Sci., 36, pp. 1265–1293.
Ranjith,  K., and Rice,  J. R., 2001, “Slip Dynamics at a Dissimilar Material Interface,” J. Mech. Phys. Solids, 49, pp. 341–361.
Achenbach,  J. D., and Epstein,  H. I., 1967, “Dynamic Interaction of a Layer and a Half-Space,” J. Eng. Mech. Div., EM5, pp. 27–42.
Adams,  G. G., 1996, “Self-Excited Oscillations in Sliding With a Constant Friction Coefficient—A Simple Model,” ASME J. Tribol., 118, pp. 819–823.
Adams,  G. G., and Nosonovsky,  M., 2000, “Contact Modelling—Forces,” Tribol. Int., 33, pp. 431–442.
Westergaard,  H. M., 1939, “Bearing Pressures and Cracks,” ASME J. Appl. Mech., 6, pp. A49–A53.
Shtaerman, I., Ya, (Steuermann, E.), 1949, Contact Problem in the Theory of Elasticity, Gostehizdat, Moscow (in Russian).
Dundurs,  J., Tsai,  K. C., and Keer,  L. M., 1973, “Contact Between Elastic Bodies With Wavy Surfaces,” J. Elast., 3, pp. 109–115.
Kuznetsov,  E. A., 1985, “Effect of Fluid Lubricant on the Contact Characteristics of Rough Elastic Bodies in Compression,” Wear, 157, pp. 177–194.
Kuznetsov,  E. A., 1976, “Periodic Contact Problem for Half-Plane Allowing for Forces of Friction,” Soviet Applied Mechanics, 12, pp. 37–44.
Nosonovsky,  M., and Adams,  G. G., 2000, “Steady State Frictional Sliding of Two Elastic Bodies With a Wavy Contact Interface,” ASME J. Tribol., 122, pp. 490–495.
Wolfram, S., 1999, The Mathematica Book, Fourth Ed., Cambridge University Press, Cambridge, UK.
Salant,  R. F., and Flaherty,  A. L., 1995, “Elastohydrodynamic Analysis of Reverse Pumping in Rotary Lip Seals With Microasperities,” ASME J. Tribol., 117, pp. 53–59.
Gel’fand, I. M., and Shilov, G. E., 1964, Generalized Functions, 1 , Academic Press, New York.
Adams,  G. G., 2001, “An Intersonic Slip Pulse at a Frictional Interface Between Dissimilar Materials,” ASME J. Appl. Mech., 68, pp. 81–86.
Zharii,  O. Y., 1996, “Friction Contact Between the Surface Wave and a Rigid Strip,” ASME J. Appl. Mech., 63, pp. 15–20.
Erdogan,  F., and Gupta,  G. D., 1972, “On the Numerical Solution of Singular Integral Equations,” Q. Appl. Math., 29, pp. 525–534.

Figures

Grahic Jump Location
Sliding of a flat elastic half-space upon a wavy elastic half-space
Grahic Jump Location
Frequency of vibration divided by 4π versus the contact zone half-length (generalized Rayleigh waves possible)
Grahic Jump Location
Frequency of vibration divided by 4π vs. the contact zone half-length (generalized Rayleigh waves do not exist)
Grahic Jump Location
Contact pressure for the frictionless case, μ12=1,ν12=0.25,κ2=0.667
Grahic Jump Location
Degree of instability divided by the friction coefficient and sliding velocity versus the contact zone length for small friction and sliding velocity

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