Symmetry, cusp bifurcation and chaos of an impact oscillator between two rigid sides

Both the symmetric period n-2 motion and asymmetric one of a one-degree- of-freedom impact oscillator are considered.The theory of bifurcations of the fixed point is applied to such model,and it is proved that the symmetric periodic motion has only pitchfork bifurcation by the analysis of the symmetry of the Poincarémap.The numerical simulation shows that one symmetric periodic orbit could bifurcate into two antisymmet- ric ones via pitchfork bifurcation.While the control parameter changes continuously, the two antisymmetric periodic orbits will give birth to two synchronous antisymmetric period-doubling sequences,and bring about two antisymmetric chaotic attractors subse- quently.If the symmetric system is transformed into asymmetric one,bifurcations of the asymmetric period n-2 motion can be described by a two-parameter unfolding of cusp, and the pitchfork changes into one unbifurcated branch and one fold branch.     

STOCHASTIC DISCRETE MODEL OF TWO-STAGE ISOLATION SYSTEM WITH RIGID LIMITERS

The possible intermittent impacts of a two-stage isolation system with rigid limiters have been investigated. The isolation system is under periodic external excitation disturbed by small stationary Gaussian white noise after shock. The maximal impact Poincare map is proposed based on the multi-body dynamics with unilateral constrains. Then in the period after shock, the zero order approximate stochastic discrete model and the first order approximate stochastic model are developed. The real isolation system of an MTU diesel engine is used to evaluate the established model. After calculating of the numerical example, the effects of noise excitation on the isolation system are discussed. The results show that the property of the system is complicated due to intermittent impact. The difference between zero order model and the first order model may be great. The effect of small noise is obvious. The results may be expected useful to the naval designers.     

SMALE HORSESHOES AND CHAOS IN DISCRETIZED PERTURBED NLS SYSTEMS(Ⅰ)—POINCAR MAP

Introduction Formanyyears,theexistenceofchaoticbehaviorindynamicalsystemshasreceived muchattention.Theoreticalandexperimentalmethodstoshowtheexistenceofchaoshave beenwelldeveloped.Itiswell knownthatifthestableandunstablemanifoldsofa hyperbolicperiodicorbi…     

SMALE HORSESHOES AND CHAOS IN DISCRETIZED PERTURBED NLS SYSTEMS(Ⅱ)—SMALE HORSESHOES

2000MathematicsSubjectClassification:35Q Introduction ContinueRef.[1],inthispart,weapplythegeneralizedConley Moserconditions[2]toshowtheexistenceofSmalehorseshoesinbelowthediscreteNLSsystems(1).Considerthefollowingn particle(any2相似文献   

The double mode model of the chaotic motion for a large deflection plate

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｌａｓｔｄｅｃａｄｅｈａｓｗｉｔｎｅｓｅｄｔｈｅｉｎｃｒｅａｓｉｎｇａｄｖａｎｃｅｓｉｎｔｈｅｓｔｕｄｙｏｆｃｈａｏｔｉｃｖｉｂｒａｔｉｏｎｏｆｍｅｃｈａｎｉｃａｌｓｙｓｔｅｍｓ．Ｈｏｗｅｖｅｒ,ｇｒｅａｔａｔｅｎｔｉｏ...     

NONLINEAR STABILITY FOR EADY'S MODEL

IntroductionEady’smodelisanimportantexampleof 3_dimensionalcontinuouslystratifiledquasi_geostrophicmotion[1].Recently ,someresultsofnonlinearstabilityforEady’smodelwereobtained[2 ,3],wheretheresultofRef.[3 ]istheimprovementofRef.[2 ] ,suchthattheresultisthebestinsomesense[4 ].Inthispaper,theresultofRef.[3 ]isimprovedbyestablishinganenhancedPoincar啨ｔｙｐｅｉｎｔｅｇｒａｌｉｎｅｑｕａｌｉｔｙ .ThenewresultshowsthatthenecessaryandsufficientlinearstabilityconditionforEady’smodelisalsothesu…     

NONLINEAR STABILITY FOR EADY＇S MODEL

IntroductionEady’smodelisanimportantexampleof 3_dimensionalcontinuouslystratifiledquasi_geostrophicmotion[1].Recently ,someresultsofnonlinearstabilityforEady’smodelwereobtained[2 ,3],wheretheresultofRef.[3 ]istheimprovementofRef.[2 ] ,suchthattheresultisthebestinsomesense[4 ].Inthispaper,theresultofRef.[3 ]isimprovedbyestablishinganenhancedPoincar啨ｔｙｐｅｉｎｔｅｇｒａｌｉｎｅｑｕａｌｉｔｙ .ThenewresultshowsthatthenecessaryandsufficientlinearstabilityconditionforEady’smodelisalsothesu…     

CHAOTIC MOTION OF A NOLINEAR THERMO_ ELASTIC ELLIPTIC PLATE

ＩｎｔｒｏｄｕｃｔｉｏｎＦｏｒａｌｏｎｇｔｉｍｅｔｈｅｅｆｆｅｃｔｏｆｔｅｍｐｅｒａｔｕｒｅｏｎｔｈｅｖｉｂｒａｔｉｏｎｏｆｐｌａｔｅｓｈａｓｄｒａｗｎｇｒｅａｔａｔｔｅｎｔｉｏｎｉｎｔｈｅｆｉｅｌｄｏｆａｅｒｏｎａｕｔｉｃｓａｎｄａｓｔｒｏｎａｕｔｉｃｓ，ｃｈｅｍｉｓｔｒｙ，ｎｕｃｌｅａｒｐｏｗｅｒａｎｄｍｅｃｈａｎｉｃａｌｅｎｇｉｎｅｅｒｉｎｇ．Ｉｎｃｏｒｒｅｓｐｏｎｄｉｎｇｔｈｅｏｒｅｔｉｃａｌａｎａｌｙｓｉｓｔｈｅｎｏｎｌｉｎｅａｒｅｆｆｅｃｔｓｈｏｕｌｄｂｅｔａｋｅｎｉｎｔｏｃｏｎｓｉ…     

Analysis of limit cycle oscillations of a typical airfoil section with freeplay

A typical airfoil section system with freeplay is investigated in the paper. The classic quasi-steady flow model is applied to calculate the aerodynamics, and a piecewise-stiffness model is adopted to characterize the nonlinearity of the airfoil section’s freeplay. There are two critical speeds in the system, i.e., a lower critical speed, above which the system might generate limit cycle oscillation, and an upper critical one, above which the system will flutter. Then a Poincaré map is constructed for the limit cycle oscillations by using piecewise-linear solutions with and without contact in the system. Through analysis of the Poincaré map, a series of equations which can determine the frequencies of period-1 limit cycle oscillations at any flight velocity are derived. Finally, these analytic results are compared to the results of numerical simulations, and a good agreement is found. The effects of freeplay value and contact stiffness ratio on the limit cycle oscillation are also analyzed through numerical simulations of the original system. Moreover, there exist multi-periods limit cycle oscillations and even complicated "chaotic" oscillations may occur, which are usually found in smooth nonlinear dynamic systems.     

GENERALIZED VECTOR VARIATIONAL-TYPE INEQUALITIES IN FC-SPACES

A class of generalized vector variational-type inequality problems (GVVTIP) are studied in FC-spaces, which includes the most of vector equilibrium problems, vector variational inequality problems, generalized vector equilibrium problems and generalized vector variational inequality problem as special cases. By using F-KKM theorem, some new existence results for GVVTIP are established in noncompact FC-space. As consequences, some recent known results in literature are obtained under much weaker assumption.     

SMALE HORSESHOES AND CHAOS IN DISCRETIZEDPERTURBED NLS SYSTEMS(Ⅰ)—POINCARÉ MAP

The existence of Smale horseshoes for a certain discretized perturbed nonlinear Schroedinger （NLS） equations was established by using n-dimensional versions of the Conley-Moser conditions. As a result, the discretized perturbed NLS system is shown to possess an invadant set A on which the dynamics is topologically conjugate to a shift on four symbols.     

Weighted Cebysev-Ostrowski type inequalities

In account of the famous Cebysev inequality, a rich theory has appeared in the literature. We establish some new weighted Cebysev type integral inequalities. Our proofs are of independent interest and provide new estimates on these types of inequalities.     

G-凸空间的择一原理和极大极小不等式

Using a fixed point theorem by Kuo, Jeng and Huang, we obtain in G-convex spaces a very general intersection theorem concerning the values of three maps. From this result we derive successively alternative theorems concerning maximal elements, analytic alternatives and minimax inequalities.     

On the selection of trial functions in the methd of weighted residuals

The principles of selecting trial functions in method of weighted residuals (MWR) are discussed by the method of functional analysis and the approximation theory of complex function in this paper. In addition, a detailed discussion is made on completeness. On this basis the concept of basic factor is proposed for the question of combinatorial structures and some basic factors and general combinatorial types of trial functions are deduced. Finally a rectangular stiffened plate is taken as an example for comparative calculation and good results have been obtained.     

Persistence of Poincaré mappings in functional differential equations (with application to structural stability of complicated behavior)

A theorem on the dependence of Poincaré mappings for different functional differential equations (FDEs) on the right-hand side of the equation is proved. Together with recent results on hyperbolic sets for noninvertible mappings, this is used to describe how Poincaré mappings and their complicated behavior in the neighborhood of a transversal homoclinic orbit persist under FDE perturbations of the equation. The method is shown to apply to three example equations, where Poincaré mappings with such behavior are known to exist.     

Some new fixed point theorems in probabilistic metric spaces

ＳＯＭＥＮＥＷＦＩＸＥＤＰＯＩＮＴＴＨＥＯＲＥＭＳＩＮＰＲＯＢＡＢＩＬＩＳＴＩＣＭＥＴＲＩＣＳＰＡＣＥＳｚｈｕＣｈｕａｎ－ｘｉ（朱传喜）（ＭａｔｈｅｍａｔｉｅｓＤｉｖｉｓｉｏｎ,Ｎａｎｃｈａｎｇ．Ｕｎｉｖｅｒｓｉｔｙ,Ｎａｎｃｈａｎｇ）（Ｒｅｃｅｉｖ...     

Stability of a cubic functional equation in intuitionistic random normed spaces

In this paper, the stability of a cubic functional equation in the setting of intuitionistic random normed spaces is proved. We first introduce the notation of intuitionistic random normed spaces. Then, by virtue of this notation, we study the stability of a cubic functional equation in the setting of these spaces under arbitrary triangle norms. Furthermore, we present the interdisciplinary relation among the theory of random spaces, the theory of intuitionistic spaces, and the theory of functional equations.     

加权残值法在钢筋混凝土拱桥非线性有限元分析中的应用

本文用圆弧梁离散拱肋;用圆柱拖带坐标、三次位移插值函数及平截面假定来描述单元位形;用加权残值配点法来消除曲梁单元的剪力与膜力闭锁。按基于连续介质力学的Ｕ．Ｌ．列式建立单元增量平衡方程,以考虑几何非线性。假定钢筋为理想弹塑性材料。按三参数各向同性强化塑性模型,建立混凝土的弹塑性本构矩阵。将拱单元分段分块,根据钢筋及砼的本构特性,建立拱单元及梁段单元的弹塑性刚度矩阵,以考虑材料非线性。用编制的程序对两座模型拱桥进行计算,计算结果与模型测试结果接近     

Coincidence point theorems in probabilistic metric spaces with a convex structures

ＣＯＩＮＣＩＤＥＮＣＥＰＯＩＮＴＴＨＥＯＲＥＭＳｉＮＰＲＯＢＡＢＩＬＩＳＴＩＣＭＥＴＲＩＣＳＰＡＣＥＳＷＩＴＨＡＣＯＮＶＥＸＳＴＲＵＣＴＵＲＥＳＷｅｅＴａｅＰａｒｋ（朴渭汰）ＫｅｕｎＳａｅｎｇＰａｒｋ（朴根生）ＹｅｏｌＪｅＣｈｏ（赵烈济）（Ｄｅｐａｒ...     

Existence and uniqueness of solutions for initial value problems of second order ordinary differential equations in Banach spaces

IntroductionLet(E,l'I)denotearealBanachspacewithapartialorderintroducedbyanormalconeKofE.Inthispaper,weshallconsiderthefollowinginitialvalueproblemofsecondorderordinarydifferentialequation(IVP):wheref:JxEZ~EandJ=LO,TiforT>0.AfunctionxeCI(J,E)issaidtobeasolutionofIVP(I)ifithasabsolutelycontinuousfirstderivativeandsatisfies(I)fora.e.teJ.Theuseofmonotonemethodsinthestudyoftheinitial(boundary)valueproblemsofordinarydiffferentialequationshasrecentlybeenquiteextensive(see,forexample[I~8]…