Frequency control of singularly perturbed forced Duffing's oscillator
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.
Cite
@article{arxiv.1709.01318,
title = {Frequency control of singularly perturbed forced Duffing's oscillator},
author = {Robert Vrabel and Marcel Abas},
journal= {arXiv preprint arXiv:1709.01318},
year = {2017}
}
Comments
12 pages with 7 figures; The final publication is available at Springer via doi.org/10.1007/s10883-011-9125-0