论同源随机激励及其响应的特点

本文从一般情形出发，为同源随机激励提出一个含义较广的定义。同源随机激励的特点是其功率谱矩阵可表示为一个列阵与其共轭行阵的乘积。在同源激励作用下，常参数线性系统的响应仍保持激励的上述特点，充分利用这一特点可以节约计算工作量。文中还借助模态分析给出了在同源平稳随机激励下响应功率谱矩阵的解析式，以及在同源演变随机激励下非平稳响应的演变谱表示式。     

关于虚拟激励法的一个注记

从具有随机频率与随机相位的随机谐和函数出发,证明了当随机频率与相位均为均匀分布而随机幅值与功率谱密度平方根成正比时,该随机过程的功率谱即精确地等于目标功率谱.进而表明:只需遍历频率区间,即可由单一谐和函数激励下的响应幅值给出响应的功率谱密度,从而揭示了虚拟激励法的物理意义.研究还表明:为了给出结构响应的功率谱密度,实际...     

同源演变随机激励下的非平稳响应

在复模态分析与演变谱分析的基础上任意点的三维坐提出了时不变线性系统的在一般演变随机的激励下的时变均方响应的一个简便实用解法。并以简化模型为例，用本方法考察了变速车辆的路面响应问题。     

基于小波-Galerkin方法的结构随机动力响应功率谱的确定

在最近发展的周期广义谐和小波PGHW(Periodic Generalized Harmonic Wavelet)的基础上,通过小波-Galerkin方法推导得到了线性单自由度结构的随机动力响应功率谱密度。在此过程中,利用PGHW的解析形式及其在频域内的特殊性:(1)推导得出了PGHW的联系系数(Connection Coefficient)的解析形式;(2)基于PGHW及其联系系数,利用小波-Galerkin方法推导得到了线性单自由度系统在确定性激励下的响应;(3)得到了在具有演变功率谱的随机动力激励下单自由度线性振子的随机响应功率谱解答。数值算例表明,无论是确定性响应解答,还是随机动力响应的功率谱密度,小波-Galerkin法的计算结果均能较好地吻合数值解。     

多点非均匀调制演变随机激励下结构地震的响应

针对大跨度结构在非均匀调制演变随机激励作用下,考虑行波效应时的非平衡随机地震响应问题,应用虚拟激励法进行了分析,由于虚拟激励法自动计及了参振振型的互相关项以及激励之间的互相关项,理论上是精确解,时变功率谱的计算采用精细逐步积分格式,使计算效率进一步得到提高。     

谐和与随机噪声联合作用下非线性系统的响应

研究了Duffing振子在谐和与随噪声联合激励下的响应和稳应性问题。用谐波平均法分析了系统在确定性谐和激励和随机激励联合作用下的响应,用随机平均法讨论了随机扰动项对系统晌应的影响。在一定条件下,系统具有两个均方响应值和跳跃现象。数值模拟表明本文提出的方法是有效的。     

非均匀调制随机激励下系统的非平稳响应分析

基于时域复模态分析，提出一种非均匀调制随机激励下系统非平稳响应特性的解析解法，用Ｎｉｉｇａｔａ地震激励模型作了说明．算例与仿真结果吻合良好．     

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     

车辆-轨道系统垂向随机振动的辛方法分析

将轨道视为无限长的周期结构,建立车辆轨道垂向耦合模型. 使用虚拟激励法将随机的轨道不平顺激励转化为确定性的简谐激励,再用辛数学方法求解轨道结构的频率响应特性和耦合系统的响应功率谱. 整个计算模型只有26个自由度,求解过程快速而精确.数值算例中,将该方法与常规有限元方法进行了比较,验证了方法的高效性和正确性,讨论了车辆速度对系统随机响应的影响.      

爆破地震地面运动的演变功率谱密度函数分析

按照Priestly提出的演变随机过程理论，对非平稳随机过程的演变功率谱密度函数进行了理论推导，并给出了定义。在此基础上，建立了基于均匀调制随机过程的爆破地震动演变功率谱密度函数。经对比发现，理论模型计算值与实验测试结果具有较好的一致性。     

Evolutionary model of finite-strain thermoelasticity

The equation of state of finite-strain thermoelasticity is obtained using a formalized approach to constructing constitutive relations for complex media under the assumption of closeness of intermediate and current configurations. A variational formulation of the coupled thermoelastic problem is proposed. The constitutive equation, the heat-conduction equation, the relations for internal energy, free energy, and entropy, and the variational formulation of the coupled problem of finite-strain thermoelasticity are tested on the problem of uniaxial extension of a bar. The model adequately describes experimental data for elastomers, such as entropic elasticity, temperature inversion, and temperature variation during an adiabatic process. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 184–196, May–June, 2008.     

Global Attractors of Evolutionary Systems

An abstract framework for studying the asymptotic behavior of a dissipative evolutionary system with respect to weak and strong topologies was introduced in Cheskidov and Foias (J Differ Equ 231:714–754, 2006) primarily to study the long-time behavior of the 3D Navier-Stokes equations (NSE) for which the existence of a semigroup of solution operators is not known. Each evolutionary system possesses a global attractor in the weak topology, but does not necessarily in the strong topology. In this paper we study the structure of a global attractor for an abstract evolutionary system, focusing on omega-limits and attracting, invariant, and quasi-invariant sets. We obtain weak and strong uniform tracking properties of omega-limits and global attractors. In addition, we discuss a trajectory attractor for an evolutionary system and derive a condition under which the convergence to the trajectory attractor is strong.     

双向固定网格渐进结构优化方法

近年来发展的渐进结构优化方法是一种有前途的结构拓扑和形状优化方法.本文在渐进结构优化方法的框架内建立了统一敏感度的概念,并基于固定网格有限元技术,发展了一种新的增加材料技术,提出了双向固定网格渐进结构优化方法.将该方法应用于复合材料壳结构开孔形状优化,以孔周等Tsai-Hill强度值作为优化目标,可以得到合理的最优解,证明了双向固定网格渐进结构优化方法的适用性.不同的初始点能得到几乎相同的最优解,展示了本文方法良好的全局最优性.     

Universal Laws in Application to Evolutionary Economics

The purpose of the present paper is to reveal some conformities to natural universal laws allowing to advance the theory of evolutionary economics. The second law of thermodynamics, Le Chatelie–Brown principle as universal laws are applied for nonlinear dynamical economic systems. The ergodic hypothesis is applied for dynamical economic systems as one from principles of economic forecasting. From the point of view of statistical physics, entropy is applied as universal function of a condition for economic systems. The evolution of economic dynamical systems at macro and microeconomic levels from the point of view of thermodynamics, statistical physics, and diffusion processes is investigated. The law of money circulation is formulated as one of the forms of display of energy conservation law in economic space. The concept of parametric economic space is introduced. The concepts of energy and number of degrees of freedom of a dynamical economic system allow substantiated cause and effect connections between the evolution of the system and a number of economic factors (forces), influencing on the system (degree of an openness, freedom of an economic system). The character of the development of technologies and the product life cycle are investigated as a nonlinear economic process. The concept of a wave function describing a technological wave connected with the entropy of a system of economic cells is introduced.     

Introduction to the Special Issue: Evolutionary Economics

Nonlinear Dynamics, Psychology, and Life Sciences -     

Smooth Stable and Unstable Manifolds for Stochastic Evolutionary Equations

Invariant manifolds are fundamental tools for describing and understanding nonlinear dynamics. In this paper, we present a theory of stable and unstable manifolds for infinite dimensional random dynamical systems generated by a class of stochastic partial differential equations. We first show the existence of Lipschitz continuous stable and unstable manifolds by the Lyapunov–Perrons method. Then, we prove the smoothness of these invariant manifolds.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday.     

Nonstationary Process: Nonstationary Bifurcation Maps,Evolutionary Dynamics

The study presented in this paper is one of a series of paperspublished by the authors on nonstationary problems. It addresses itselfto the characterization of the types of dynamical responses and theirranges contained in the time flow of the Duffing nonlinear,nonstationary, dissipative, forced oscillator. A new effective method –a Nonstationary Bifurcation Map (EI-Lu map) – has been introduced bythe authors that allows us to do precisely this. This new technique isby far more advantageous than the customary methods in use: the phaseportrait or Poincaré maps. The latter may give inadequate informationbecause of the overlapping dynamical responses contained within rangesof time. The main feature of nonstationary processes is that thenonstationary responses are transient. The phenomena of the transiencyare presented in detail. Significant cases are those when thenonstationary transmission of the signals crosses differentnonstationary bifurcation boundaries. This is significant because mostof dynamical-biological activities occur in the regions between orderand chaos. It characterizes nonstationary dynamical processes. Thepossibility of constructing responses for arbitrary small nonstationaryinputs may be used as nonstationary perturbations, replacing customaryperturbations of integrable Hamiltonians.     

Wave Dynamics of Saturated Porous Media and Evolutionary Equations

Nonlinear wave dynamics of an elastically deformed saturated porous media is investigated following the Biot approach. Mathematical models under research are the Biot model and its generalization by consideration of viscous stresses inside liquids. Using two-scales and linear WKB methods, the classical Biot system is transformed to a first-order wave equation. To construct the solution of the other system, an asymptotic modified two-scales method is developed. Initial system of equations is transformed to a nonlinear generalized Korteweg–de Vries–Burgers equation for quick elastic wave. Distinctions of wave propagation in the context of the Biot model and its generalization are shown.     

Evolutionary solutions to the brachistochrone problem with Coulomb friction

The classical brachistochrone problem was originally proposed by Johann Bernoulli more than 300 years ago, and is still one of the most elegant problems in modern mathematics. This paper examines a generalisation of the original brachistochrone problem by the inclusion of a non-conservative force in the form of Coulomb friction. Solutions to this problem are found using an evolutionary computational technique based on Darwinian natural selection and survival of the fittest. These evolutionary solutions tend to indicate that as friction is introduced the optimum curves develop from cycloidal (the analytical solution for the conservative problem) toward straight lines. The flexibility of the evolutionary method to optimise for other objectives is then discussed.