The nonlinear dynamics of a single-degree-of-freedom oscillator with an external excitation and complex non-viscous damping is examined. The complex nature of the damper introduces a hidden variable to the set of equations of motion. We examine nonlinear oscillations, bifurcations and the escape from the potential well in that system. The shape of the resonance curve is obtained by the multiple time scales method and it is confirmed numerically. By treating the excitation and damping effects as perturbations we found the heteroclinic orbits connecting the saddle points of the Hamiltonian and estimate the range of system parameters leading to a chaotic behaviour by means of the Melnikov method. This result is also confirmed by numerical simulations. The mechanism of escape from the potential well is analyzed by means of behaviour charts and basins of attraction.
Nonlinear oscillations, transition to chaos and escape in the Duffing system with non-classical damping
RUZZICONI, LAURA;
2011-01-01
Abstract
The nonlinear dynamics of a single-degree-of-freedom oscillator with an external excitation and complex non-viscous damping is examined. The complex nature of the damper introduces a hidden variable to the set of equations of motion. We examine nonlinear oscillations, bifurcations and the escape from the potential well in that system. The shape of the resonance curve is obtained by the multiple time scales method and it is confirmed numerically. By treating the excitation and damping effects as perturbations we found the heteroclinic orbits connecting the saddle points of the Hamiltonian and estimate the range of system parameters leading to a chaotic behaviour by means of the Melnikov method. This result is also confirmed by numerical simulations. The mechanism of escape from the potential well is analyzed by means of behaviour charts and basins of attraction.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
