Frequency control of singularly perturbed forced Duffing's oscillator

TL;DR

This paper investigates the control of high-frequency nonlinear oscillations in a singularly perturbed forced Duffing oscillator, introducing a new analytical method based on dynamic coordinate changes.

Contribution

It presents a novel approach for analyzing nonlinear oscillations in the Duffing oscillator using dynamic coordinate transformations, extending previous results.

Findings

Frequency can be controlled by a small parameter in the highest derivative.

The new method provides analytical approximations for large amplitude oscillations.

Generalizations of earlier results on Duffing oscillations are demonstrated.

Abstract

We analyze the dynamics of the forced singularly perturbed differential equation of Duffing's type. We explain the appearance of the large frequency nonlinear oscillations of the solutions. It is shown that the frequency can be controlled by a small parameter at the highest derivative. We give some generalizations of results obtained recently by B.S. Wu, W.P. Sun and C.W. Lim, Analytical approximations to the double-well Duffing oscillator in large amplitude oscillations, Journal of Sound and Vibration, Volume 307, Issues 3-5, (2007), pp. 953-960. The new method for an analysis of the nonlinear oscillations which is based on the dynamic change of coordinates is proposed.