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.
出版日期
2014年01月11日(中国期刊网平台首次上网日期,不代表论文的发表时间)