Modified Lindstedt-Poincar＆#233; Method for Obtaining Resonance Periodic Solutions of Nonlinear Non-autonomous Oscillators-中国期刊网

摘要 AmodifiedLindstedt-Poincaré(LP)methodforobtainingtheresonanceperiodicsolutionsofnonlinearnon-autonomousvibrationsystemsisproposedinthispaper.Inthemodifiedmethod,nonlinearnon-autonomousequationsareconvertedintoagroupoflinearordinarydifferentialequationsbyintroducingasetofsimpletransformations.Anapproximateresonancesolutionfortheoriginalequationcanthenbeobtained.Theperiodicsolutionsofprimary,super-harmonic,sub-harmonic,zero-frequencyandcombinationresonancescanbesolvedeffectivelyusingthemodifiedmethod.Someexamples,suchasdampedcubicnonlinearsystemsundersingleanddoublefrequencyexcitation,anddampedquadraticnonlinearsystemsunderdoublefrequencyexcitation,aregiventoillustrateitsconvenienceandeffectiveness.UsingthemodifiedLPmethod,thefirst-orderapproximatesolutionsforeachequationareobtained.Bycomparison,themodifiedmethodproposedinthispaperproducesthesameresultsasthemethodofmultiplescales.

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Modified Lindstedt-Poincar＆#233; Method for Obtaining Resonance Periodic Solutions of Nonlinear Non-autonomous Oscillators

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Modified Lindstedt-Poincar＆#233; Method for Obtaining Resonance Periodic Solutions of Nonlinear Non-autonomous Oscillators

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