Computing periodic solutions for a CD-player with impact using piecewise linear shooting

This paper consists of two contributions in the field of nonlinear systems: (1) the introduction of a piecewise linear shooting algorithm, and (2) an analysis of the periodic behavior of a CD-player under harmonic excitation. Compared to a single shooting algorithm, which does not explicitly account for the piecewise linear nature of the CD-player model, the piecewise linear shooting algorithm can provide a significant decrease in computational effort. Namely, the transition times are efficiently solved by Henon´s method after detecting a regime crossing. Consequently, the integration-step refinement, typically encountered when using ODE routines, is avoided as much as possible. With piecewise linear shooting, the periodic behavior of a CD-player with impact is studied as a function of both the excitation frequency and amplitude. It is shown that the rich dynamic behavior such as encountered in experiments largely justifies the usage of a single degree-of-freedom piecewise linear model