Averaging method for strongly nonlinear oscillators with periodic excitations
type: Item
instance of: scholarly article
title: Averaging method for strongly nonlinear oscillators with periodic excitations
zbMATH Open document ID: 0813.70014
DOI: 10.1016/0020-7462(94)90068-X
author: R. Valéry Roy
published in: International Journal of Non-Linear Mechanics
publication date: 1995-05-28T00:00:00Z
review text: An averaging method is developed to predict periodic solutions of strongly nonlinear and harmonically forced oscillators. The analysis is restricted to the case of period-1 orbits. The original governing equation is transformed into an autonomous set of differential equations governing the energy and resonant phase variables. The form of the transformation is given by the unperturbed conservative orbits of the system. The scheme is applied to three examples, the nonlinear pendulum, the single-well Duffing oscillator, and the canonical escape oscillator. For these examples, the analysis is performed by using Jacobian elliptic functions.
Mathematics Subject Classification ID: 70K40
Mathematics Subject Classification ID: 34C29
Mathematics Subject Classification ID: 34C15
zbMATH DE Number: 707512
zbMATH Keywords: periodic solutions
zbMATH Keywords: single-well Duffing oscillator
zbMATH Keywords: canonical escape oscillator
zbMATH Keywords: Jacobian elliptic functions
MaRDI profile type: Publication
full work available at URL: 0020-7462(94)90068-x
OpenAlex ID: W2113583936
description: scientific article; zbMATH DE number 707512