Open Access
2012 An Analytical Approximation Method for Strongly Nonlinear Oscillators
Wang Shimin, Yang Lechang
J. Appl. Math. 2012: 1-9 (2012). DOI: 10.1155/2012/958121


An analytical method is proposed to get the amplitude-frequency and the phase-frequency characteristics of free/forced oscillators with nonlinear restoring force. The nonlinear restoring force is expressed as a spring with varying stiffness that depends on the vibration amplitude. That is, for stationary vibration, the restoring force linearly depends on the displacement, but the stiffness of the spring varies with the vibration amplitude for nonstationary oscillations. The varied stiffness is constructed by means of the first and second averaged derivatives of the restoring force with respect to the displacement. Then, this stiffness gives the amplitude frequency and the phase frequency characteristics of the oscillator. Various examples show that this method can be applied extensively to oscillators with nonlinear restoring force, and that the solving process is extremely simple.


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Wang Shimin. Yang Lechang. "An Analytical Approximation Method for Strongly Nonlinear Oscillators." J. Appl. Math. 2012 1 - 9, 2012.


Published: 2012
First available in Project Euclid: 14 December 2012

MathSciNet: MR2889112
zbMATH: 1334.70037
Digital Object Identifier: 10.1155/2012/958121

Rights: Copyright © 2012 Hindawi

Vol.2012 • 2012
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