文档介绍：强非线性振动的GLP算法构建与实现专业: 计算机软件与理论硕士生: 陈海雯指导老师:梁华金副教授中文摘要本文簇于{#线一登振豌L-P方法豹理论,提出雄广熬L-P方法(GLP方法), 8适用于强j}线性振动分析,并采用计算机代数方法,构建和实现算法,代《上需要人工推导的复杂运算,求出系统的符号化的解析解。 i先,介绍非线性振动经典的L-P算法,应用计算机代数方法对非线性振动 l行分据。采霸MATHE[糖TICA进专亍簿法擒建,实现计算梳代数簸理,完成符錾。￡次,提出邋舍于强非线性振动分析的GLP算法并采用MATHEMATICA进行算§。该算法通过引进一个参数变换,把原来对于大参数(旧参数)是强非线性《,转换成对于小参数(新参数)是弱非线性的系统,然后再应用经典的L-P l论遴行求解。各求解箨除摄动解豹遭稷中,闲靖考虑齐次方程韵遴鼹和菲≯程蛇特解。 l着,把适用于单自由度系统自由振动的GLP算法搬广到二自由度系统的强 E强迫振动。#倒证明GLP法对疆菲线性振动系统的有效毪和准确性,也充分体现出现代 t{弋数怒嚣寐繁复懿手工推簿经过计算撬符号运算变餐较磊易举翁饶点。￡文的部分研究成果已经撰写成多篪论文,其中有2麓分别被力学程计算机 j核心刊物《振动与冲击》和《现代计算机》录用,待发表。其余的将向力 2的杂志投稿。强非线性振动、、GLP方法、MATHEMATICA、计算机代数方法、符号运算第l 更 The Construction andImplementation ofGLP Algorithm forStrongly Nonlinear Vibration Major: Computer Software and TheoD, Name: Chen珏aiwen Supervisor:Associate Professor Liang Huajin Abst ract Based on thetheory oftheL-P method innonlinear vibration,a generalized L-P (GLP)method ispresented inthisthesisfortheanalysis ofstrollIgly nonlinear method isconstructedandimplemented byusing puter algebra toreplace plex manual work inderiving analytic solution of thesystem therefore can beobtained by means ofsymbol operation. Firstly,the L—Pmethod innonlinear vibration isintroduced,puter algebra isused toanalyze the nonlinear vibrationsystem。nle MATHEN"LTICA software is used toconstruct thealgorithm andimplement thesymbol operation. Secondly,a generalized L-P(GLP)method ispresented and constructed by introducing a parameter strongly nonlinear system corresponding to a largeparameter(original parameter)can be transformed into aweakly nonlinear system、vith respect to asmallparameter赫ew parameter)。Then the classical L-P method Can beused tosolve solving theperturbation differentialequation,both ofthegeneral solution ofthe homogeneous equation and thespecial solution ofnon-homogeneous equation are considered. Thirdly,the GLP method for freevibration ofone-degree-of-freedom system is generalized toforcedvibra