The forced chaotic and irregular oscillations of the nonlinear two degreesof freedom (2DOF) system

The behavior of a 2DOF nonlinear mechanical system excited by a pure harmon ic force is studied by the first approximation (averaging and asymptotic) m ethod and by numerical simulations. The response curves, instability domains, displacement versus time dependen cies and phase plane portraits are determined. By means of the first approx imation solution are find three instability domains, where jumps occur, or in which the beats, irregular and chaotic motions emerge. The numerical simulations confirm these properties, but shaw that there exi st several new bifurcations and instability domains, in which the response on the pure harmonic excitation is chaotic. The response curve of the low d amped system has in the first resonance the multifold solution. The corresp onding oscillations depend on the history, i.e. on the way and the speed of the very slow exciting frequency variation, at which the system comes into the current state. The responses at increasing or decreasing frequencies d iffer, the hysteresis loops exist.