A new perturbation algorithm for strongly nonlinear oscillators

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dc.contributor.authorPakdemirli M.
dc.contributor.authorKarahan M.M.F.
dc.contributor.authorBoyaci H.
dc.date.accessioned2024-07-22T08:21:14Z
dc.date.available2024-07-22T08:21:14Z
dc.date.issued2009
dc.description.abstractA new perturbation algorithm combining the Method of Multiple Scales and Lindstedt-Poincare techniques is proposed. The algorithm combines the advantages of both methods. Convergence to real solutions with large perturbation parameters can be achieved for both constant amplitude and variable amplitude cases. Three problems are solved: Linear damped vibration equation, classical duffing equation and damped cubic nonlinear equation. The new method does not violate the main assumption of perturbation series that correction terms should be much smaller than the leading terms. It is proven that for arbitrarily large perturbation parameter values, correction terms remain much smaller that the leading terms. Results of Multiple Scales, new method and numerical solutions are contrasted. The proposed new method produces much better results for strong nonlinearities.
dc.identifier.urihttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/18520
dc.language.isoEnglish
dc.subjectControl nonlinearities
dc.subjectConstant amplitude
dc.subjectCorrection terms
dc.subjectDamped vibrations
dc.subjectDuffing equations
dc.subjectLeading terms
dc.subjectMethod of multiple scale
dc.subjectMultiple scale
dc.subjectNumerical solution
dc.subjectPerturbation parameters
dc.subjectPerturbation series
dc.subjectReal solutions
dc.subjectStrong nonlinearity
dc.subjectStrongly nonlinear oscillator
dc.subjectVariable amplitudes
dc.subjectAlgorithms
dc.titleA new perturbation algorithm for strongly nonlinear oscillators
dc.typeConference paper

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