摘 要非线性振动理论在工程科学中有着广泛的应用,同时从非线性振动中提出的一些数学模型,例如:Duffing方程,vanderpol方程和Mathieu方程,在非线性动力学理论中占有很重要的地位。本文应用了多尺度方法对小参数非线性微分方程求近似解。同时这也是全文的核心。全文共分四章。首先,第一章叙述了分线性振动的由来,分类和特点,对振动现象的普遍存在进行了系统的描述。第二章非线性振动理论的研究方法简单介绍了解析法和小参数的引入,并着重叙述了近似解析法中的一种常用的方法—多尺度法。第三章运用多尺度法求一类非线性微分方程的近似解。最后一章结束语总结全文,述说本文的写作感受。全文重点在二,三章,详细说明多尺度法,利用多尺度法通过对非线性微分方程近似解的求导,解出近似解。关键词:非线性振动,多尺度法,稳定性,周期解,AdjusttoreachagreementofdealyVanderPolequationAbstractTheoryofnonlinearvibrationcanbeapplybroadlyinthe engineeringscience field,and some mathematical model advance from nonlinear vibration,forexample:Duffingequation,Vanderpol equation and Mathieu equation, it lay hold on very important place inthetheory ofnonlinear vibration field. The discourse broadmultiplesizemethodfor little parameter nonlineardifferential equation count proximate itiscore of the discourse have four first, The first chapter narrative cause ofnonlinearvibration,classificationandspecially characteristic,for vibration phenomena universal presence ongoing systemic second chapterinvestigationmethodintheory of nonlinear vibration simpleintroduce analyze method and draw into little parameter,and emphasize monly use methodin proximate analyze method investigation method------multiple size third chapter alone degree of pulsory vibration proximate disentangle discuss make use of multiple size method disentangle special nonlinear differential in resonance and noresonance two cases proximate disentangle. The last chaptertally up full text, recount writing feel important point of the full text in the second chapterand the third chapter,elaborateon multiple size method,and makeuseofpass nonlinear differential proximate disentangle proximate consequence binationsketch,forexample noresonancephenomenon,secondresonancephenomenon,Beyondharmonicwave resonanceand secondharmonicwave :proximate disentangle,nonlinear vibration,multiple size method,mainresonance,目录摘 要
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