Dynamics of friction oscillators excited by moving base and/or driving force.

The response of a single-degree-of-freedom system with dry friction under a constant velocity of the base and/or harmonic driving force is analyzed via either closed-form or numerical approaches. The first main purpose of this paper is to investigate the influence of the base speed on the system response. To this end, in the case of a moving base with and without a harmonic driving force, as a new result, closed-form solutions are presented under the assumption of Coulomb's friction law, including a static coefficient different from the kinetic one. In more detail the existence of a critical base velocity is proved, which is the lower bound of no-stick and base-velocity-independent motions. The second main purpose of this paper is to investigate the influence of friction modelling on the system response. To this end, the results achieved via the Coulomb's law are compared with those obtained via a particular velocity-dependent friction law; the proposed law allows the static coefficient to exponentially decay to the kinetic one, still preserving the discontinuity at null relative speed. The purpose at hand has also been accomplished by using standard numerical methods