共查询到20条相似文献,搜索用时 15 毫秒
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In this paper, a new procedure is proposed to construct the stationary probability density for a family of the single-degree-of-freedom (SDOF) strongly non-linear stochastic second-order dynamical systems subjected to parametric and/or external Gaussian white noises. First of all, the Fokker-Planck-Kolmogorov (FPK) equation associated with the original Itô stochastic differential equation is replaced by the equivalent FPK equation by adding arbitrary anti-symmetric diffusion coefficient. Then, a family of invariant measures depending on the arbitrary anti-symmetric diffusion coefficient and another arbitrary function is constructed by vanishing the probability flows in two directions. Finally, the drift vector associated with a family of Itô stochastic differential equations is deduced by giving, a priori, these two arbitrary functions. It is shown that the known invariant measures dependent on energy are only the special cases of invariant measures presented in this paper, while some other classes of invariant measures are independent of energy. Thus, the invariant measures constructed in this paper are those belonging to the most general class of the SDOF strongly non-linear stochastic second-order dynamical systems so far. 相似文献
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非比例阻尼线性体系平稳随机地震响应计算的虚拟激励法 总被引:5,自引:0,他引:5
应用复振型分解方法,将非比例阻尼线性体系在地震作用下的动力方程求解问题转化为若干个广义复振子的求解与叠加问题。通过假定地震地面运动为一零均值的平稳随机激励,应用虚拟激励法原理,推导得到了广义复振子动力坐标的解析计算公式,进而得到了以复振型为基础的非比例阻尼线性体系随机地震响应计算的一般实数解析解答。算例证实了这种方法的可靠性及高效率。 相似文献
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随机载荷是工程结构在服役中经常承受的一种复杂的载荷形式,通常采用统计学特性对其进行描述。对随机载荷作用下的结构进行拓扑优化设计是一项极具挑战性的工作,其主要难点在于,(1) 传统隐式拓扑优化方法的设计变量数巨大,且用于结构动态性能拓扑优化问题时存在虚假模态等数值不稳定问题; (2) 对结构的随机动力响应统计量及其灵敏度进行计算需要极大的计算量; (3) 隐式拓扑优化框架下的分析模型与优化模型强耦合,导致结构有限元模型具有极高的自由度,进一步加剧了上述困难。本文基于移动可变形组件框架和虚拟激励法理论,提出了一种平稳随机载荷作用下结构的显式拓扑优化设计方法。通过将一系列可移动和可变形的结构组件作为优化的基础单元,实现了使用少量设计变量描述结构拓扑构型的目的。采用虚拟激励法、自由度删除技术和模态位移法有效降低了对结构进行随机振动分析和灵敏度分析的计算量。在此基础上,以结构柔顺度的标准差为目标函数、以设计域内实体材料的体积为约束条件,实现了限带白噪声作用下结构的拓扑优化设计,并通过数值算例验证了本文方法的有效性。 相似文献
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We derive an analytical solution to the stress concentration factor (kt) for slightly roughened random surfaces. Topology is assumed to possess Gaussian distribution of heights and auto correlation length, ACL . For our development, we combine Gao’s first-order perturbation method, the Hilbert transform, and an energy conservation principal related to the Parseval theorem.The root-mean-square (RMS) value of kt results in a function of the ratio RMS-roughness to ACL. The derived formula agrees with experimental results previously reported. The results provide insight for more efficient design. 相似文献
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In this paper,two kinds of asymptotic analytic expression of the Brusselator limitcycle are given by means of two simple methods.To some extem,they are better thanthe analytic expression in [2]. 相似文献
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I.IntroductionRalldomvibrationoftenoccursinpracticalellgilleeringproblclllsl'l.Forexalllple,theunevellroadexcitesthewheelwithuncertainnZagnitudeandirregulartimelapseandresultsinrandonlvibrationofvehicle,whcllsufferingfromearthquakeor11urricallc,tilestructurewillvibraterandomly.Thewaytostudyrandomvibrationisusillgmathematicaltool,randomprocessestheory,todcalwithvibrationproblem,soitisveryilnporlant1'L,r1.alldomvibrationstudyingtostudytilel.andolllprocesses.Genel'ally.thestudyofrandomprocesses… 相似文献
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《Comptes Rendus Mecanique》2017,345(12):844-867
In this paper, we characterize random eigenspaces with a non-intrusive method based on the decoupling of random eigenvalues from their corresponding random eigenvectors. This method allows us to estimate the first statistical moments of the random eigenvalues of the system with a reduced number of deterministic finite element computations. The originality of this work is to adapt the method used to estimate each random eigenvalue depending on a global accuracy requirement. This allows us to ensure a minimal computational cost. The stochastic model of the structure is thus reduced by exploiting specific properties of random eigenvectors associated with the random eigenfrequencies being sought. An indicator with no additional computation cost is proposed to identify when the method needs to be enhanced. Finally, a simple three-beam frame and an industrial structure illustrate the proposed approach. 相似文献
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I.IntroductionHertzintroducedtheconceptofnon-holonomics}stems(NHS)in1894ti].HeconsideredthatHamiltoll'sprinciple\"asnotsatisfiedforNHSandinparticulardidnotyieldLagrangeequationswithundeterminedmultipliers.Forthisfeason.Hblderl=],Suslovi3]andVoronetzl']dev… 相似文献
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Based on the theory of Euler-Bernoulli beam and Winkler assumption for elasticfoundation,a mathematical model is presented.By using Fourier transformation for spacevariable,Laplace transformation for time variable and convolution theorem for theirinverse transformations,a general solution for dynamical problem of infinite beam on anelastic foundation is obtained.Finally,the cases of free vibration,impulsive response andmoving load are also discussed. 相似文献
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Bas van der Vorst E. Matthijs Toose Dirk van den Ende Rob J. J. Jongschaap Jorrit Mellema 《Rheologica Acta》1995,34(3):274-280
A theory analogue to tha of Rouse is given, to describe the rheological behavior of dilute solutions consisting of clusters of crosslinked polymers. The frequency-dependent behavior of the dynamic moduli of these fluids differs substantially from that of the well-known Rouse-like fluid (GG1/2). In our case the storage modulus becomes proportional to 3/2, while the loss modulus is proportional to . The loss modulus dominates the dynamic behavior for frequencies smaller than the largest normal frequency of the clusters. 相似文献
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This paper investigates the probability density function (PDF) of non-linear random ship roll motion using a previously developed path integration method. The mathematical model of ship rolling motion consists of a linear-plus-cubic damping and a non-linear restoring moment in the form of odd-order polynomials up to fifth-order terms. In the path integration method, the interpolation scheme is based on the Gauss–Legendre quadrature integration rule and the short-time transition probability density function is formulated by short-time Gaussian approximation. The present work extends the path integration method to the case of non-linear random ship roll motion. Different values of non-linearity coefficient and excitation intensity are used to examine the effectiveness of the path integration method. Numerical analysis shows that the results of the path integration method agree well with the simulation results, even in the tail region. The path integration method is effective and it is simply implemented in the examined cases. Due to the presence of non-linear damping terms and non-linear restoring moment terms, the PDFs of roll angle and angular velocity exhibit highly non-Gaussian behaviors. 相似文献
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This paper is devoted to the construction and to the identification of a probabilistic model of random fields in the presence of modeling errors, in high stochastic dimension and presented in the context of computational structural dynamics. Due to the high stochastic dimension of the random quantities which have to be identified using statistical inverse methods (challenging problem), a complete methodology is proposed and validated. The parametric–nonparametric (generalized) probabilistic approach of uncertainties is used to perform the prior stochastic models: (1) system-parameters uncertainties induced by the variabilities of the material properties are described by random fields for which their statistical reductions are still in high stochastic dimension and (2) model uncertainties induced by the modeling errors are taken into account with the nonparametric probabilistic approach in high stochastic dimension. For these two sources of uncertainties, the methodology consists in introducing prior stochastic models described with a small number of parameters which are simultaneously identified using the maximum likelihood method and experimental responses. The steps of the methodology are explained and illustrated through an application. 相似文献
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Igor Kukavica 《Journal of Dynamics and Differential Equations》1991,3(4):611-618
In the case of solutions of the two-diensional Navier-Stokes equations, the following analyticity property is established. If the initial datum lies on the global attractor and is close enough to a stationary solution, then the analyticity radius att = 0 of the solution can be made arbitrarily large. 相似文献
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Nonlinear dynamical systems, being more of a realistic representation of nature, could exhibit a somewhat complex behavior. Their analysis requires a thorough investigation into the solution of the governing differential equations. In this paper, a class of third order nonlinear differential equations has been analyzed. An attempt has been made to obtain sufficient conditions in order to guarantee the existence of periodic solutions. The results obtained from this analysis are shown to be beneficial when studying the steady-state response of nonlinear dynamical systems. In order to obtain the periodic solutions for any form of third order differential equations, a computer program has been developed on the basis of the fourth order Runge-Kutta method together with the Newton-Raphson algorithm. Results obtained from the computer simulation model confirmed the validity of the mathematical approach presented for these sufficient conditions. 相似文献
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Andrey Shilnikov 《Nonlinear dynamics》2012,68(3):305-328
In-depth understanding of the generic mechanisms of transitions between distinct patterns of the activity in realistic models
of individual neurons presents a fundamental challenge for the theory of applied dynamical systems. The knowledge about likely
mechanisms would give valuable insights and predictions for determining basic principles of the functioning of neurons both
isolated and networked. We demonstrate a computational suite of the developed tools based on the qualitative theory of differential
equations that is specifically tailored for slow–fast neuron models. The toolkit includes the parameter continuation technique
for localizing slow-motion manifolds in a model without need of dissection, the averaging technique for localizing periodic
orbits and determining their stability and bifurcations, as well as a reduction apparatus for deriving a family of Poincaré
return mappings for a voltage interval. Such return mappings allow for detailed examinations of not only stable fixed points
but also unstable limit solutions of the system, including periodic, homoclinic and heteroclinic orbits. Using interval mappings
we can compute various quantitative characteristics such as topological entropy and kneading invariants for examinations of
global bifurcations in the neuron model. 相似文献