This investigation considers the dynamic stability of the steady-state frictional sliding of a finite-thickness elastic layer pressed against a moving rigid and flat surface of infinite extent. The elastic layer is fixed on its bottom surface; on its entire top surface, the rigid surface slides with constant speed and with a constant friction coefficient. The plane-strain equations of motion for a linear isotropic elastic solid are solved analytically for small dynamic disturbances. The analysis shows that even with a constant (speed-independent) friction coefficient, the steady solution is dynamically unstable for any finite friction coefficient. Eigenvalues with positive real parts lead to self-excited vibrations which occur for any sliding speed and which increase with increasing coefficient of friction. This is in contrast to the behavior of an elastic half-space sliding against a rigid surface in which the instability only occurs if the coefficient of friction is greater than unity. This work and its extensions are expected to be relevant in the theoretical aspects of sliding friction as well as in a variety of areas such as earthquake motion and brake dynamics.
Self-Excited Oscillations of a Finite-Thickness Elastic Layer Sliding Against a Rigid Surface With a Constant Coefficient of Friction
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received October 27, 2017; final manuscript received November 28, 2017; published online December 12, 2017. Assoc. Editor: Kyung-Suk Kim.
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Mohammadi, N. K., and Adams, G. G. (December 12, 2017). "Self-Excited Oscillations of a Finite-Thickness Elastic Layer Sliding Against a Rigid Surface With a Constant Coefficient of Friction." ASME. J. Appl. Mech. February 2018; 85(2): 021005. https://doi.org/10.1115/1.4038640
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