Abstract
Recent research has shown that energy losses named as ‘relaxation damping’ can occur even with an infinite coefficient of friction using the method of dimensional reduction (MDR) which is strictly applicable to axis-symmetric elastic contact problems. If the solution with infinite coefficient of friction is regarded as a limiting case of ‘very large’ friction, this limiting solution is often useful because it will typically be much simpler than that obtained assuming a finite coefficient of friction, and it is likely to give reasonable estimates for the actual dissipation in cases that are far from the gross slip (sliding) limit. Using the advantage of relaxation damping, we shall give a generalized proof that is independent of the MDR. We shall also extend the proof to problems in which the applied loads follow a general trajectory in three-dimensional vector space. Further, we shall demonstrate how the energy dissipation per cycle varies with an increasing normal force, showing that relaxation damping could be useful as a limit in cases where there is significant variation in a normal force.
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