Role of nonlinear dissipation in soft Duffing oscillators

The effect of a strictly dissipative force (velocity to the pth power model) on the response and bifurcations of driven, soft Duffing oscillators is considered. The method of harmonic balance is used to obtain the steady state harmonic response. An anomalous jump in the harmonic response (signifying a break in the resonance curve), obtained in the case of linearly damped, soft Duffing oscillators, is shown to persist even in the presence of nonlinear damping. It is shown that the bifurcation structure and the structure of the chaotic attractor are quite insensitive to the damping exponent p. However, the threshold values of the parameters, at which bifurcations occur, depend both on the damping index and the damping coefficient. The Melinkov criterion and an analytical criterion for the period-doubling bifurcation have been obtained in the presence of combined linear and cubic damping.