Vibration analysis of an oscillator with non-smooth dry friction constraint

Global vibrational behaviour of a single degree-of-freedom (SDOF) oscillator subjected to Coulomb type of dry frictional constraint and harmonic excitation is investigated in this paper. To obtain a numerical solution to the non-smooth dynamical problem, the equation of motion is discretized in the time domain by means of the implicit Bozzak-Newmark scheme. An algebraic equation governing the current state of the system is obtained in terms of its velocity. Utilizing the fact that the frictional constraint can be completely characterized by two scenarios - (i) forward sliding or stiction with a tendency to move forward, and (ii) backward sliding or stiction with a tendency to move backward, two coupled linear complementary equations are deduced. With the reduction of the non-smooth dynamical problem to a linear complementarity problem (LCP) in terms of supremum velocities and slack forces, the rapid and endless switches from sliding to stiction, and vice versa, in a vibration problem, are automatically detected and handled effectively. This is superior to the event-based methods and analytical methods available in the literature. Numerical results obtained using the proposed method are compared with the analytical solutions for harmonically excited dry-friction oscillator with ordinary behaviour; excellent agreement is observed. The proposed method is then employed for determining the global chaotic and deterministic behaviour of a harmonically excited dry-friction oscillator with system and excitation parameters varying in wide ranges.