随机剪切柱在地震激励下的演变随机响应

随机剪切柱是指固连于地面的剪切柱的某些物理参数是随机变量 ,该模型在Niigata地震激励下的响应属于演变随机响应。本文将新近发展起来的演变随机响应问题的统一解法 ,推广到用于求解随机结构振动响应问题。首先用这一方法求出每个样本结构的随机响应 ,然后用MonteCarlo法来进一步求随机结构的集合随机响应特性。这样 ,与单纯用Monte Carlo法进行数字模拟相比 ,可使计算工作量大为减少。本文用随机剪切柱的演变随机响应问题加以说明     

Bounds on the Probability of Failure in Random Vibration

A new method to construct upper and lower bounds for the failure probability of a structure exposed to random excitations is presented. The method is based on an extension of the classical inclusion-exclusion series of Rice where the main idea is to take into consideration only realizations which are in the safe area at a number of previous instants of time. By a numerical example it is demonstrated that this method may lead to rather sharp bounds.     

Optimal Bounded Control of First-Passage Failure of Quasi-Integrable Hamiltonian Systems with Wide-Band Random Excitation

The optimal bounded control of quasi-integrable Hamiltonian systems with wide-band random excitation for minimizing their first-passage failure is investigated. First, a stochastic averaging method for multi-degrees-of-freedom (MDOF) strongly nonlinear quasi-integrable Hamiltonian systems with wide-band stationary random excitations using generalized harmonic functions is proposed. Then, the dynamical programming equations and their associated boundary and final time conditions for the control problems of maximizinig reliability and maximizing mean first-passage time are formulated based on the averaged Itô equations by applying the dynamical programming principle. The optimal control law is derived from the dynamical programming equations and control constraints. The relationship between the dynamical programming equations and the backward Kolmogorov equation for the conditional reliability function and the Pontryagin equation for the conditional mean first-passage time of optimally controlled system is discussed. Finally, the conditional reliability function, the conditional probability density and mean of first-passage time of an optimally controlled system are obtained by solving the backward Kolmogorov equation and Pontryagin equation. The application of the proposed procedure and effectiveness of control strategy are illustrated with an example.     

The Failure of Rank-One Connections

This article is concerned with interface problems for Lipschitz mappings f ₊:? ⁿ ₊→? ⁿ and f _?:? ⁿ _?→? ⁿ in the half spaces, which agree on the common boundary ? ^{n ? 1}=?? ⁿ ₊=?? ⁿ _?. These naturally occur in mathematical models for material microstructures and crystals. The task is to determine the relationship between the sets of values of the differentials Df ₊ and Df _?. For some time it has been thought that the polyconvex hulls [Df ₊] ^pc and [Df _?] ^pc satisfy Hadamard's jump condition or are at least rank-one connected. Our examples here refute this idea.The estimates of the Jacobians we obtain in the course of solving the so-called Monge-Ampère inequalities seem also to be of independent interest. As an application, we construct uniformly elliptic systems of first order partial differential equations in the same homotopy class as the familiar Cauchy-Riemann equations, for which the unique continuation property fails.     

The Linear Boltzmann Equation in Column Experiments of Porous Media

Transport in Porous Media - The use of the linear Boltzmann equation is proposed for transport in porous media in a column. By column experiments, we show that the breakthrough curve is reproduced...     

迟滞系统受随机激励的响应计算

首先为随机激励设计了具有较高精度的滤波器，把迟滞系统受有色噪声激励的随机振动问题转化为由迟滞系统与滤波器组成的扩阶系统受白噪声激励的随机振动问题，然后详细论述了等效线性化法对此问题的具体求解，着重推导了高斯随机变量联合矩的递推关系和李亚普诺夫方程解法的实现，最后根据数字模拟结果分析了等效线性化法的精度和误差来源，给出了迟滞减振系统参数设计的有关建议。     

Random attractors

In this paper, we generalize the notion of an attractor for the stochastic dynamical system introduced in [7]. We prove that the stochastic attractor satisfies most of the properties satisfied by the usual attractor in the theory of deterministic dynamical systems. We also show that our results apply to the stochastic Navier-Stokes equation, the white noise-driven Burgers equation, and a nonlinear stochastic wave equation.     

Column buckling under friction

Summary The buckling problem of a cantilever column is discussed when the axial loading device introduces friction forces. Adopting global stability criteria and applying the bifurcation theory to the present non-conservative eigenvalue problem, the critical load is defined and the post-critical behavior is investigated.

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Stabknickung unter Reibungseinfluß

Übersicht Die Ausknickung einer eingespannten Säule wird diskutiert, wobei durch die axiale Belastungsvorrichtung Reibungskräfte aufgebracht werden. Unter der Annahme eines globalen Stabilitätskriteriums und der Verwendung der Verzweigungstheorie wird die kritische Last des Systems und sein nachkritisches Verhalten untersucht.

     

高速瓦楞辊的磨损失效分析

本文对进口的高速瓦楞辊的磨损失效形式进行了分析，认为其主要磨损形式是磨粒磨损，即齿侧为滑动磨粒磨损，齿底为应变疲劳磨粒磨损，而齿预则包括了这两种磨损形式；齿顶和齿根两侧都是磨损最严重的部位；磨粒主要是纸中夹带的ＳｉＯ２砂粒。文章最后还明确指出，瓦楞辊的返修期应当定在其出现非均匀磨损之前，但是由于楞齿承受曲应力而诱发疲劳裂纹，故此返修次数是有限的。     

窄带随机噪声激励下多自由度非线性系统的响应

在随机振动的研究中，研究较多的是系统在宽带噪声作用下的响应问题，对于非线性系统特别是多自由度非线性系统在窄带随机噪声作用下的响应问题则研究较少。本文研究了三自由度非线性系统在窄带随机噪声激励下的主共振响应和稳定性问题。用多尺度法分离了系统的快变项，给出了系统响应的振幅和相位角满足的方程。用摄动法讨论了系统随机项对系统响应的影响。当随机扰动较小时，在一定的参数范围内，对应于不同的初值，系统具有两个均方响应值，随机饱和现象也存在。当随机扰动增大时，系统可从一个大的响应突跳为一个小的响应，或从一个小的响应突跳为一个大的响应，即存在随机跳跃现象。数值模拟表明本文提出的方法是有效的。     

单自由度系统的爆炸地震演变响应

提出了一个单自由度结构系统爆炸地震随机地面振动演变响应的理论分析方法。根据爆炸地震效应的特点 ,建立了一个地面运动激励模型 ,并以TNT炸药爆炸实验测试结果为实例 ,讨论了模型中相关基本参数的确定方法及其结果。在给定结构固有频率和阻尼系数条件下 ,得到了单自由度系统的爆炸地震位移响应功率演变谱和均方根位移理论解。与在一个混凝土基座上的测试结果进行对比表明 ,得到的理论均方根位移具有较好的预测精度。     

Random perturbations of bifurcation diagrams

Random perturbations of one dimensional bifurcation diagrams can exhibit qualitative behavior that is quite different from that of the unperturbed, deterministic situation. For Markov solutions of one dimensional random differential equations with bounded ergodic diffusion processes as perturbations, effects like disappearance of stationary Murkov solutions (break through), slowing down, bistability, and random symmetry breaking can occur. These effects are partially the results of local considerations, but as the perturbation range increases, global dynamics can alter the picture as well. The results are obtained via the analysis of stationary solutions of degenerate Markov diffusion processes, of stationary, non-Markovian solutions of stochastic flows, and of Lyapunov exponents of stochastic flows with respect to steady states.     

柔性桩沉降的随机特性

本文采用小波动方法结合剪切位移法,将土体弹性模量视为沿深度方向的一维随机场,推导出了柔性桩桩顶沉降响应方差上限的解析表达式。通过算例探讨了四种不同相关函数及相关距离对桩身沉降及桩身应力响应方差的影响。得出了指数型相关函数较其它三种的计算值明显偏小;当竖向相关距离大于桩长时其变化对桩顶沉降响应方差影响不大的结论。     

Random perturbations of parametric autoresonance

Nonlinear Dynamics - We consider a system of two nonlinear differential equations describing the capture into autoresonance in nonlinear oscillators under small parametric driving. Solutions with...     

工程结构的随机特征问题研究及其在梁结构中的应用

采用子结构模态综合和摄动随机有限元相结合求解工程结构的随机特征问题。为求出随机特征对的方差，借助于模态截断概念推出诸特征值与特征向量对随机变量的偏导数。以染结构为典型算法，定量研究了子结构动模态的选取个数与随机特征对的计算精度间关系，以梁的长细比首次确定使用Timoshenko梁和Euler-Bernoulli梁两模型求解梁类工程结构随机特征问题的适用范围。     

Effective Medium Analysis of Random Lattices

Calculations of effective conductivities of generalized random bond lattices representing porous media are compared to approximations using effective medium theory (EMT). We use numerical simulations of flow through 2D and 3D random lattice models, which allow for variable lattice densities and a lognormal distribution of local conductivities, to compare effective conductivities to effective medium approximations. We find that the analytical expressions provide good agreement to the simulations in 2D systems, but are in significant error in 3D systems when the standard deviation of the local conductivities is large.     

Random Vibration of Strongly Nonlinear Systems

Procedures developed recently to extend the quasi-conservativeaveraging method to the case of non-white broad-band excitations arefurther extended and presented in a unified framework. The excitationscan be stationary or nonstationary with known evolutionary spectra, andthey can be additive, or multiplicative, or both. Relative merits ofthese procedures are compared, and their accuracies are substantiated byMonte Carlo simulations.     

Random excitation of nonlinear coupled oscillators

This paper presents the experimental results of random excitation of a nonlinear two-degree-of-freedom system in the neighborhood of internal resonance. The random signals of the excitation and response coordinates are processed to estimate the mean squares, autocorrelation functions, power spectral densities, and probability density functions. The results are qualitatively compared with those predicted by the Fokker-Planck equation together with a non-Gaussian closure scheme. The effects of system damping ratios, nonlinear coupling parameter, internal detuning ratio, and excitation spectral density level are considered in both studies except the effect of damping ratios is not considered in the experimental investigation. Both studies reveal similar dynamic features such as autoparametric absorber effect and stochastic instability of the coupled system. The experimental results show that the autocorrelation function of the coupled system has the feature of ultra narrow band process and degenerates to a periodic one as the internal detuning departs from the exact internal resonance condition. The measured probability density functions of the response of the main system suggests that the Gaussian representation is sufticient as long as the excitation level is relatively low in the neighborhood of the system internal resonance condition.     

The Conjugacy of Stochastic and Random Differential Equations and the Existence of Global Attractors

We consider stochastic differential equations in d-dimensional Euclidean space driven by an m-dimensional Wiener process, determined by the drift vector field f₀ and the diffusion vector fields f₁,...,f_m, and investigate the existence of global random attractors for the associated flows . For this purpose is decomposed into a stationary diffeomorphism given by the stochastic differential equation on the space of smooth flows on R^d driven by m independent stationary Ornstein Uhlenbeck processes z¹,...,z^m and the vector fields f₁,...,f_m, and a flow generated by the nonautonomous ordinary differential equation given by the vector field (_t/x)^–1[f₀(_t)+ _i=1 ¹ f_i(_t)z _t ⁱ ]. In this setting, attractors of are canonically related with attractors of . For , the problem of existence of attractors is then considered as a perturbation problem. Conditions on the vector fields are derived under which a Lyapunov function for the deterministic differential equation determined by the vector field f₀ is still a Lyapunov function for , yielding an attractor this way. The criterion is finally tested in various prominent examples.