Coulomb friction oscillator : Modelling and responses to harmonic loads and base excitations

Abstract In this paper we revisit a mass–spring–friction oscillator, where the friction refers to Coulomb's perfect dry contact friction. We refine the model formulation of the friction force and find that the equation of motion of the oscillator is a two-phase linear system with a slide-stick switch, rather than the usual three-phases equations. Also we obtain a simple slide–slide condition. Then the exact solution of the response to simple harmonic loading is obtained. With the aid of the long-term behavior of the exact solution, the steady motions of the oscillator with 0, 1, 2, 4, 6, 8, 10, 12, 14 stops per cycle are categorized in the parametric space of the ratios of forces and frequencies. Stops of zero duration are further classified into two types: normal stops and abnormal stops, the criteria of which are also given.

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