Dynamics of Piecewise Linear Oscillators

This chapter presents a review of previous analytical work on the dynamics of periodically excited piecewise linear oscillators. The common characteristic of these oscillators is that their stiffness and damping properties may change abruptly at specific displacement values. First, an analytical method is presented for determining periodic steady-state response of these oscillators. This analysis takes advantage of the fact that the exact solution form for any solution piece, included within any time interval where the stiffness and damping properties of the oscillator remain constant, is known. Then, an appropriate methodology is also presented, revealing the stability properties of the located periodic motions. This methodology is based on the derivation of a matrix relation which determines how an arbitrary but small perturbation at the beginning of a periodic solution propagates to the end of a response period. Then, some useful results obtained by bifurcation analysis of the periodic solutions are also derived. Finally, typical numerical results are presented, by considering example mechanical models.