On the response of a preloaded mechanical oscillator with a clearance: Period-doubling and chaos

The dynamic behavior of a harmonically excited, preloaded mechanical oscillator with dead-zone nonlinearity is described quantiatively. The governing strongly nonlinear differential equation is solved numerically. Damping coefficient-force ratio maps for two different values of the excitation frequency have been formed and the boundaries of the regions of different motion types are determined. The results have been compared with the results of the forced Duffing's equation available in the literature in order to identify the differences between cubic and dead-zone nonlinearities. Period-doubling bifurcations, which take place with a change of any of the system parameters, have been found to be the most common route to chaos. Such bifurcations follow the scaling rule of Feigenbaum.b half length of the clearance.