Response of an oscillator with a Duffing parameter of the fifth power

Abstract

Quintic Duffing oscillator is considered. Amplitude-phase relations are derived using averaging theorem and perturbation methods. First The forced quintic system is studied. Stability regions are com-pared to the general case with quintic-qubic non-linearity. Numerical results show that Perturbationmethod and averaging are in agreement with each other for a range of frequency values. For first or-der perturbation the Lindstedt-Poincaré technique is reduced to the multiple scales method. Onlywhen both linearities are taken into account, five solutions are present. Magnitudes of non-linearityinput plays a role in observing region of unstable solutions.