Resonant locking in viscous and dry friction damper kinematically driving mechanical oscillators

The present paper analyzes the dynamics of some simple models of a mechanical vibratory system kinematically driven by dry and nonlinear viscous friction dampers. Three different types of models of the mechanical system, viz., single and two degrees-of-freedom linear systems and a single degree-of-freedom Duffing oscillator are considered in the article to explore the dynamics of dry friction driven oscillation. Through detailed analysis it is shown that such systems can lock with the oscillating friction slider, particularly around wide frequency bands near the resonances of mechanical systems. Such a phenomenon is termed as the resonant locking in the present paper. The analytical results are substantiated by direct numerical simulations. Finally a slightly general case is analyzed where a simple system is considered to be driven by a nonlinear damper (pth power damper). Resonant locking is found to exist also for a nonlinear damper driven system.