A Contribution on Forced Periodic Oscillations With Piecewise Linear and Constant Damping

Abstract

In control system design and precision mechanics it is important to know the precise motion of excited or self-excited vibration under the influence of dry friction. In this paper, the motion of such a nonlinear oscillator is analyzed with the aid of pointmappings. As an example, a nonlinear function of damping dependent on the velocity can be approximated by piecewise linear functions. For this example, the stability of periodic solutions of the type q (t+T/2) = −q(t), (T = period, t = time), is discussed. The case of “critical stability” leads to potential points of bifurcation (branching-off solutions) which are investigated. Calculated examples are compared with experiments.