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1.
A. N. Kounadis 《Archive of Applied Mechanics (Ingenieur Archiv)》1996,66(6):395-408
Summary Nonlinear dynamic buckling of nonlinearly elastic dissipative/nondissipative multi-mass systems, mainly under step load of infinite duration, is studied in detail. These systems, under the same loading applied statically, experience a limit point instability. The analysis can be readily extended to the case of dynamic buckling under impact loading. Energy, topological and geometrical aspects for the total potential energyV, which is constrained to lie in a region of phase-space whereV0, allow conclusions to be drawn directly regarding dynamic buckling. Criteria leading to very good, approximate and lower/upper bound dynamic buckling estimates are readily established without solving the highly nonlinear set of equations of motion. The theory is illustrated with several analyses of a two-degree-of-freedom model. 相似文献
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提出了一种非线性系统周期解的延拓算法。指出了非线性系统周期解在分岔点处由于雅可比矩阵奇异而导致一般延拓方法延拓失败问题;然后基于推广的打靶法的思想,将普通延拓算法推广,提出了一种用于周期解延拓的算法。对于非线性动力系统,该算法可以在已知某一参数下的周期解的基础上,求解出在一定参数范围内非线性动力系统的解随参数的连续变化情况。应用该方法对非线性柔性转子-轴承系统的周期解与参数的依赖关系进行了求解,验证了方法的有效性。 相似文献
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I.IntroductionInordertostudybifurcationsofnonlineardynamicalsystemsinthedegeneratecasesofhighercodimensionnumber(>3),wemustcomputenormalformsofhigherorderfornonlineardynamicalsystems.Inrecenttwentyyearsmanyscientistsmadeveryimportantcontributionstodevelop… 相似文献
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Based on the new explicit Magnus expansion developed for nonlinear equations defined on a matrix Lie group, an efficient numerical method is proposed for nonlinear dynamical systems. To improve computational efficiency, the integration step size can be adaptively controlled. Validity and effectiveness of the method are shown by application to several nonlinear dynamical systems including the Duffing system, the van der Pol system with strong stiffness, and the nonlinear Hamiltonian pendulum system. 相似文献
5.
Tian Li-xin 《应用数学和力学(英文版)》1994,15(10):973-980
In the present paper we study the maximum dissipative extension of Schrodingeroperator.introduce the generalized indefinite metvic space and get the representation ofmaximum dissipative extension of Schrodinger operator in natural boundary space.make preparation for the further study longtime chaotic behaxior of infinite dimensiondynamics system in nonlinear Schrodinger equation. 相似文献
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IntroductionWiththedevelopmentintheapplicationsofnonlinearsciencetheories,bifurcationsofdynamicalsystemsinengineeringandtechnologyhavebeeninvestigatedwidely ,especiallyfortheperiodicsolutionresponse.Manyscientistshavedonealotofinterestingworksinthisare… 相似文献
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The dynamical character for a perturbed coupled nonlinear Schrodinger system with periodic boundary condition was studied. First, the dynamical character of perturbed and unperturbed systems on the invariant plane was analyzed by the spectrum of the linear operator. Then the existence of the locally invariant manifolds was proved by the singular perturbation theory and the fixed-point argument. 相似文献
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A generalized hyperbolic perturbation method is presented for homoclinic solutions of strongly nonlinear autonomous oscillators,in which the perturbation procedure is improved for those systems whose exact homoclinic generating solutions cannot be explicitly derived.The generalized hyperbolic functions are employed as the basis functions in the present procedure to extend the validity of the hyperbolic perturbation method.Several strongly nonlinear oscillators with quadratic,cubic,and quartic nonlinearity are studied in detail to illustrate the efficiency and accuracy of the present method. 相似文献
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IntroductionInbiomechanics,interspecificinteractioncanbereducedtodynamicsystem ,andwecanusetwo_dimensionalnonlineardynamicsystemmodelstodescribethemechanismandthecourseofinteractionbetweentwopopulations[1,2 ,3 ] .Interspecificinteractioninvolvesnotonlyonepopulation’sefforttotheother,butalsoothereffortsfromenvironment.Accordingtointeractiomechanism ,thesedynamicsystemscanbedividedintopredator_preysystem ,competitionsystem ,beneficialsymbiosissystemandsoon ,andpredator_preysystemisalwaysvaluedm… 相似文献
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I.IntroductionAllphysicalsystemsarenonlineartosomeextent.Actually,Lineal.systemisimaginarymodelwherenonlinearfactorisomittedinnonlinearsystem.Insolvingtheautocontl'ol,nonlinearoscillationtheory,theboundarystagnationproblenloffluidIncchanicsandsollleproblemsofsemi-conducttheoryandquantummechanicsetc'.weOnlyncedtosolvethefollowingproblem,whichisnonlineardifferentialequationsystemwithtilesll,allparanletel'inhighestorderderivativeandnonlinearboundaryconditions.whereE>0isasmallparameter,teR,x,fi… 相似文献
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非线性最优控制系统的时程精细计算研究 总被引:2,自引:1,他引:2
针对非线性最优控制问题 ,通过一阶 Taylor级数展开 ,得到线性化的动力学方程 ,进而在方程原变量的基础上 ,引入对偶向量 (Lagrange乘子向量 ) ,将动力学方程从 Lagrange体系引入到了 Hamilton体系 ,在全状态下 ,从一个新的角度对非线性最优控制问题进行了描述 ,进一步基于时程精细积分理论 ,对其方程进行了有效的精细求解 ,并通过算例说明了文中方法的有效性 相似文献
13.
A new system of general nonlinear variational inclusions is introduced and studied in Banach spaces. An iterative algorithm is developed and analyzed by use of the resolvent operator techniques to find the approximate solutions of the system of general nonlinear variational inclusions involving different nonlinear operators in uniformly smooth Banach spaces. 相似文献
14.
在哈密顿体系下分析非线性动力学问题 总被引:15,自引:4,他引:15
首先将n维未知向量q的二阶非线性力系统Mq+Gq+Kq=F(q,q,t)转化为与其等价的2n维未知向量v的一阶微分方程v=Hv+f(v,t),其中非线性部分ji(v,t)=0(i=1,...n),fi(v,t)=Fi-n(q,q,t)(i=n+1,...2n);然后给出一种求解v的逐步积分公式,从而将精细积分法进一步推广应用到非线性动力学问题。算例表明本方法的计算量较小且结果合理可靠。 相似文献
15.
The relation between the Lyapunov exponent spectrum of a periodically excited non-autonomous dynamical system and the Lyapunov
exponent spectrum of the corresponding autonomous system is given and the validity of the relation is verified theoretically
and computationally. A direct method for calculating the Lyapunov exponent spectrum of non-autonomous dynamical systems is
suggested in this paper, which makes it more convenient to calculate the Lyapunov exponent spectrum of the dynamical system
periodically excited. Following the definition of the Lyapunov dimensionD
L
(A)
of the autonomous system, the definition of the Lyapunov dimensionD
L
of the non-autonomous dynamical system is also given, and the difference between them is the integer 1, namely,D
L
(A)
−DL=1. For a quasi-periodically excited dynamical system, similar conclusions are formed.
Project supported by the National Natural Science Foundation of China (No. 19772027), the Science Foundation of Shanghai Municipal
Commission of Education (99A01) and the Science Foundation of Shanghai Municipal Commission of Science and Technology (No.
98JC14032). 相似文献
16.
IntroductionandDefinitionsIn [1 ] ,ChangShishengandPengYongchengintroducedtheconceptofprobabilisticcontractorcoupleinNon_ArchimedeanPN_spaces (forshort,N .A .MengerPN_spaces) .Usingthisconcept,undertheconditiont_normΔ =min ,theystudiedtheexistenceanduniquenesso… 相似文献
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An online method of identification of dynamic characteristics only using measured ambient response of structural dynamic system is widely focused on. The Ibrahim and ARMA ( AutoRegressive Moving Average ) methods are basic identification methods. A model on dynamic system suffered by random ambient excitation was researched into, and a subspace decomposition methodwas introduced. Robustness and effectiveness of this approach on identification of vibration characteristics are demonstrated on numerical experiment. 相似文献
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This work is concerned with the use of new nunumerical methods to establish some new criteria to determine the equilibrium point's stability of a multidimensional nonlinear dynamic system. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献