Dynamics of oscillators with strongly nonlinear asymmetric damping

Dynamics of a class of strongly nonlinear single degree of freedom oscillat ors is investigated. Their common characteristic is that they possess piece wise linear damping properties, which can be expressed in a general asymmet ric form. More specifically, the damping coefficient and a constant paramet er appearing in the equation of motion are functions of the velocity direct ion. This class of oscillators is quite general and includes other importan t categories of mechanical systems as special cases, like systems with Coul omb friction. First, an analysis is presented for locating directly exact p eriodic responses of these oscillators to harmonic excitation. Due to the p resence of dry friction, these responses may involve intervals where the os cillator is stuck temporarily. Then, an appropriate stability analysis is a lso presented together with some quite general bifurcation results. In the second part of the work, this analysis is applied to several example system s with piecewise linear damping, in order to reveal the most important aspe cts of their dynamics. Initially, systems with symmetric characteristics ar e examined, for which the periodic response is found to be symmetric or asy mmetric. Then, dynamical systems with asymmetric damping characteristics ar e also examined. In all cases, emphasis is placed on investigating the low forcing frequency ranges, where interesting dynamics is noticed. The analyt ical predictions are complemented with results obtained by proper integrati on of the equation of motion, which among other responses reveal the existe nce of quasiperiodic, chaotic and unbounded motions.