On the mechanism of stick and nonstick, periodic motions in a periodically forced, linear oscillator with dry friction

In this paper, the dynamics mechanism of stick and nonstick motion for a dry-friction oscillator is discussed. From the theory of Luo in 2005 [Conumm. Nonlinear Sci. Numer Simul., 10, pp. 1-55], the conditions for stick and nonstick motions are achieved. The stick and nonstick periodic motions are predicted analytically through the appropriate mapping structures. The local stability and bifurcation conditions for such periodic motions are obtained. The stick motions are illustrated through the displacement, velocity, and force responses. This investigation provides a better understanding of stick and nonstick motions of the linear oscillator with dry friction. The methodology presented in this paper is applicable to oscillators with nonlinear friction forces.