文档介绍：摘要论文题目:梁结构的非线性振动分析学科名称:计算数学研究生:李娜指导教师:赵凤群教授摘要 UlIIII Y2346887 签名: 签名: 自然科学和工程实际中的动力学系统从本质上讲都是非线性的,非线性的动力系统一般用非线性微分方程组或者非线性差分方程组描述。由于存在非线性的因素,并且随着系统参数的不断变化,非线性系统的动力学行为将产生一系列复杂的变化,例如分岔、混沌、分形等。近年来,随着研究的深入,非线性动力学在自然科学、生物医学、工程技术领域等有着广泛的应用。本文首先学****了分岔和混沌等非线性的基本理论,然后对非保守简支梁和轴向运动梁系统的分岔与混沌行为进行了分析,具体研究内容如下: (1)对所建立的非保守简支梁系统的动力学方程,进行无量纲化后并求其数值解。分析了均布随从力的变化对扰动系统动力学行为的影响,给出全局分岔图,可以发现系统由倍周期分岔通向混沌的整个过程。给出相应的时间历程图、相图和庞加莱截面图以更具体的分析扰动系统的动力学特性。(2)推导了轴向运动梁系统的动力学方程,进行无量纲化并数值求解。分析了轴向速度的变化对系统动力学行为的影响。首先给出了系统关于轴向速度的全局分岔图,可以看出系统由周期运动通向混沌的整个过程。给出对应的时间历程图、相图和庞加莱截面图以分析系统的动力学特性。其次给出了系统对应周期运动和混沌运动的最大Lyapunov指数。关键词:简支梁;非线性振动;分岔;混沌 Title:NONLINEAR VIBRATION ANALYSIS OF BEAM STRUCTURE putational Mathematics Name:Na LI Supervisor:PrOf-Fengqun ZHAO Abstract Signature:盟 Signature: fhe dynamic system inthephysical science and theengineering practice isgenerallV nonlinear,which 1S described by nonlinear differential equations and nonlineardi饿rence equatlonS‘Because oftheexistence of nonlinear factors,with theconti肌ous variation of co廊olparameter inthesystem,the dynamic behavior ofsystem causes aseries anges,8uch as bifurcation,chaos,fractal and SO ,with thedevelopment of research,the nonlineardynamics increasingly show wide application prospects inengine嘶ng technology,biological medicine and socialscience. The dynamic characteristics ofthenonconservative simply supported be锄and theaxiallv moVlng beRITI are researchedbased onstudying nonlinear theoryknowledge,such aSbi缸cation and specific research contents are asfoilows: (J)Fhe dynamical equation ofthenonconservative simply supported be锄svstem is establlshed,theequation isprocessed dimensionless and then啪eric翻solution isca】晒ed out. jlhe change oftheuniform follower force which influence ondyn锄ic behavior ofthe perturbed system 1Sanalyzed,the global bifurcationdiagram isgiven and thentheentire procedure of period-doubling bifurcation leading to chaos of thesystem co玎esponding time history,phase portrait and Poincare sectionare