DYNAMIC BEHAVIOR AND STABILITY OF SIMPLE FRICTIONAL SYSTEMS

Numerous authors have demonstrated that problems arise over existence and uniqueness of solution in quasi-static contact problems involving large coefficients of Coulomb friction. This difficulty was greatly el ucidated by a simple two-degree-of-freedom model introduced by Klarbri ng. In the present paper, the dynamic behavior of Klarbring's model is explored under a wide range of loading conditions. It is demonstrated that the dynamic solution is always unique and deviates from the quas i-static only in a bounded oscillation for sufficiently low friction c oefficients. Above the critical coefficient, slip in one of the two di rections is found to be unstable so that the system never exists in th is state for more than a short period of time compared with the loadin g rate. In the limit of vanishing mass, these periods become infinites imal but permit unidirectional state changes with discontinuous displa cements. A revised quasi-static algorithm is developed from this limit and is shown to predict the dynamic behavior of the system within a b ounded oscillation for large coefficients of friction. (C) 1998 Elsevi er Science Ltd. All rights reserved.