The method of multiple scales for forced oscillators with some real-power nonlinearities in the stiffness and damping force

Ivana Kovacic

Chaos, Solitons & Fractals, 2011, vol. 44, issue 10, 891-901

Abstract: The steady-state response of forced damped nonlinear oscillators is considered, the restoring force of which has a non-negative real power-form nonlinear term and the linear term of which can be negative, zero or positive. The damping term is also assumed in a power form, thus covering polynomial and non-polynomial damping. The method of multiple scales with a new expansion parameter is presented in order to cover the cases when the nonlinearity is not necessarily small. Amplitude-frequency equations and approximate solutions for the steady-state response at the frequency of excitation are obtained and compared with numerical results, showing good agreement.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:44:y:2011:i:10:p:891-901

DOI: 10.1016/j.chaos.2011.07.006

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