在振动力学教材中处理混沌内容的尝试

总结在振动力学教材中处理混沌内容的尝试．分析了振动教材对混沌内容选择和处理的要求,概述教材中相关的主要内容,简要说明对混沌内容这种处理的特点．     

无簧混沌振动器

本文研究了２种无簧混沌振动器的力学模型．数值仿真和实验结果表明，其动态响应都是混沌的，且敏感依赖于初始条件．这种混沌振动器可以作为工程上宽频振动的高效振源     

圆筒连续型水轮混沌旋转的力学机制与能量演化

混沌水轮是展示混沌现象的典型力学装置,国内外众多学者对其进行了深入的研究．本文探讨了圆筒连续型水轮混沌旋转的力学机理与能量转换问题．把圆筒连续型水轮的数学模型转换为Kolmogorov系统,基于惯性力矩、内力矩、耗散力矩和外力矩的不同耦合模式,利用理论分析和数值仿真相结合方法,分析探讨了圆筒连续型水轮混沌旋转的主要影响因素和内在的力学机制．研究了水轮系统哈密顿能、动能和势能之间的相互转换．讨论了能量与Rayleigh数之间的关系．引进Casimir函数分析水轮系统的动力学行为和能量转换,并估计混沌吸引子的界．Casimir函数反映了能量转换和轨道与平衡点间的距离,数值仿真结果展现出它们之间的关系．     

单调激活函数惯性项神经耦合系统的混沌共存

混沌及其稳态共存是神经网络系统中一个重要研究热点问题．本文基于惯性项神经元模型,利用非线性单调激活函数构造了一个惯性项神经耦合系统,采用理论分析和数值模拟相结合的方法,研究了系统平衡点以及静态分岔的类型,分析了系统两种不同模式的混沌及其稳态共存．具体来说,我们通过选取不同的初始值,利用相应的相位图和时间历程图,展现了系统混沌对初值的敏感依赖性．进一步,采用耦合强度作为动力学的分岔参数,研究了混沌产生的倍周期分岔机制,得到了单调激活函数耦合下的惯性项神经元系统混沌共存现象．     

非惯性参考系中弹性薄板动力系统在纵横振动相互耦合时的全局分岔及混沌性质

讨论非惯性参考系中弹性薄板动力系统１∶１内共振时的全局分岔及其混沌性质．首先对系统的奇点进行了分析，进而得到了奇点附近同宿轨的参数方程，再用Ｍｅｌｎｉｋｏｖ方法研究了系统的同宿轨分岔及其混沌运动．研究表明，对各种不同共振情形，系统将由同宿轨分岔过渡到混沌运动．最后用数值仿真证实了理论分析的结果．     

力学系统混沌的主动控制

对混沌进行控制是将非线性科学应用于工程技术的新研究领域．本文首先综述对力学系统混沌运动进行控制的各种策略，然后讨论了实现中的关键问题，介绍了成功的实验．最后，指出了该领域中值得注意的若干问题．     

混沌振动压实动力学的仿真研究——（Ⅰ）混沌识别

本文提出了四自由度混沌振动压路机“机架-振动轮-土”系统的力学模型;建立了其数学模型;对数学模型进行了数值仿真;根据振动轮的运动,利用混沌识别的定性方法(相轨图、功率谱图和Poincare图)与定量方法(最大Lyapunov指数),对系统的混沌特征进行了识别．结果表明：系统的运动是混沌的．     

非自旋航天器混沌姿态运动及其参数开闭环控制

研究万有引力场中受大气阻力且存在结构内阻尼的非自旋航天器在椭圆轨道上平面天平动的混沌及其参数开闭环控制问题．在建立数学模型的基础上确定出现混沌的必要条件并数值验证混沌的存在性，提出非线性振动系统混沌运动的参数开闭环控制并应用于控制航天器的混沌姿态运动．     

控制系统中的混沌现象研究

本文介绍了实际控制系统中的混沌现象,并应用相轨迹、功率谱、Lyapunov指数等方法,证明了混沌现象在实际自动控制系统中的存在,并分析了产生混沌现象的原因．     

非线性强迫Mathieu方程的激变和瞬态混沌

应用广义胞映射图论（ＧＣＭＤ）方法研究了非线性强迫Ｍａｔｈｉｅｕ方程的激变、瞬态混 沌、以及随系统参数变化的全局分岔特性．揭示了参数激励常微分系统混沌吸引子的边界激变 是由于混沌吸引子与其吸引域边界上的不稳定周期轨道发生碰撞而产生的,发现了边界激变产 生的瞬态混沌,在Ｐｏｉｎｃａｒé截面上直观地表明了瞬态混沌的几何空间结构,以及瞬态混沌的空 间结构随着系统参数逐渐远离激变临界值的衰变．给出了对自循环胞集进行局部细化的方法．     

Shock waves in diatomic chains—I. linear analysis

Solutions are presented for the response of semi-infinite diatomic chains to a step jump in velocity. Integral transform theory and contour integration are used to express the solutions as definite integrals for the acoustic and optical branch contributions to the response. The contribution of an end mode is indicated for the case of particles that are unequally spaced within a unit cell. Asymptotic approximations are obtained for the contribution of the optical and acoustic branches to the wave solution when the wave propagates far into the lattice. Asymptotic estimates are obtained, also, for the discontinuous speeds at which the head of the pulse travels in a general diatomic chain. Shock profiles for the special case of a simple diatomic chain and for a general diatomic chain are discussed, and upper bounds are obtained for the maximum shock responses that are possible in such chains with the given shock condition.     

Balancing aspects of numerical dissipation,dispersion, and aliasing in time-accurate simulations

The current study looks at the selection of scheme elements that are well-suited for long-time integration of unsteady flows in the absence or under-resolution of physical diffusion. A concerted assembly of numerical components are chosen relative to a target aliasing limit, which is taken as a best-case scenario for overall spectral resolvability. High-order and optimized difference stencils are employed in order to achieve accuracy; meanwhile, quasi skew-symmetric splitting techniques for nonlinear transport terms are used in order to greatly improve robustness. Finally, tunable and scale-discriminant artificial-dissipation methods are incorporated for de-aliasing purposes and as a means of further enhancing both accuracy and stability. Central finite difference methods are considered, and spectral characterizations of the scheme components are presented. Canonical test cases (the isentropic vortex [IV] and Taylor-Green vortex problems) are chosen in order to highlight the benefits associated with the proposed approach for enhancing overall algorithm robustness and accuracy.     

Incremental elastic motions superimposed on a finite deformation in the presence of an electromagnetic field

The equations describing the interaction of an electromagnetic sensitive elastic solid with electric and magnetic fields under finite deformations are summarized, both for time-independent deformations and, in the non-relativistic approximation, time-dependent motions. The equations are given in both Eulerian and Lagrangian form, and the latter are then used to derive the equations governing incremental motions and electromagnetic fields superimposed on a configuration with a known static finite deformation and time-independent electromagnetic field. As a first application the equations are specialized to the quasimagnetostatic approximation and in this context the general equations governing time-harmonic plane-wave disturbances of an initial static configuration are derived. For a prototype model of an incompressible isotropic magnetoelastic solid a specific formula for the acoustic shear wave speed is obtained, which allows results for different relative orientations of the underlying magnetic field and the direction of wave propagation to be compared. The general equations are then used to examine two-dimensional motions, and further expressions for the wave speed are obtained for a general incompressible isotropic magnetoelastic solid.     

New results for isotropic point scatterers: Foldy revisited

Since 1945, Foldy’s method has been used to predict velocity and attenuation for various types of scatterers. In this paper, it is shown that Foldy’s method also yields predictions of reflection and transmission of scalar waves by a random distribution of point or line scatterers contained in a slab. Results are given in two and three dimensions, and for normal and oblique incidences. Formulae are also obtained for the reflection and transmission of longitudinal waves by point or line scatterers distributed in an elastic (non-viscous) fluid. Energy equations are derived, and expressions are obtained for the energy dissipated in the slab on average over one period. Curves for the reflection and transmission coefficients are presented in the case of solid cylindrical bars immersed in a fluid. The results obtained in this paper are expected to be valid for a low density of scatterers. Potential applications of this work occur in ultrasonic evaluation of materials, seismic exploration and medical ultrasonics, where reflected (or backscattered) data are used to construct maps or images of the materials (metals, composites, earth subsurface, tissue). The formulae of this work are expected to provide useful tools for better and more efficient mapping or imaging.     

Mechanical model for staggered bio-structure

A generic mechanical model for bio-composites, including stiff platelets arranged in a staggered order inside a homogeneous soft matrix, is proposed. Equations are formulated in terms of displacements and are characterized by a set of non-dimensional parameters. The displacements, stress fields and effective modulus of the composite are formulated. Two analytical models are proposed, one which includes the shear deformations along the entire medium and another simplified model, which is applicable to a slender geometry and yields a compact expression for the effective modulus. The results from the models are validated by numerical finite element simulations and found to be compatible with each other for a wide range of geometrical and material properties. Finally, the models are solved for two bio-structures, nacre and a collagen fibril, and their solutions are discussed.     

On the nonlinear mechanics of discrete networks

Summary A formulation of the equilibrium problem for nonlinear elastic networks is presented. Explicit necessary and sufficient conditions for minimum-energy configurations are derived. These are used to generate a relaxed formulation of the theory in which fibre slackening is accounted for automatically. For the relaxed problem, minimum-energy and uniqueness theorems are proved and used as the basis of a numerical method in which equilibrium configurations are recovered asymptotically in the long-time limit of an artificial dynamical problem. Such an approach is particularly useful for networks, as stiffness-based equilibrium formulations are known to suffer from ill-conditioning in a wide variety of applications. Several illustrative examples are discussed. Accepted for publication 22 June 1996     

Governing equations in non-isothermal diffusion

Generalizations of Fick's law for the diffusion flux are often considered in the literature by analogy with those for the heat flux. The paper reviews the balance equations for a fluid mixture and provides the equations for the diffusion fluxes. As a consequence, the mass densities are shown to satisfy a system of hyperbolic equations. Moreover, for a binary mixture of ideal gases in stationary conditions, Fick's law is recovered. Next, diffusion fluxes are regarded as constitutive functions and a whole set of thermodynamic restrictions are determined which account for diffusion, heat conduction, viscosity and inhomogeneities. Hyperbolic models for diffusion and heat fluxes are established which involve the co-rotational derivative. The driving term of diffusion turns out to be the gradient of chemical potential rescaled by the temperature.     

截尾Gauss概率密度函数中待定参数的确定

给出一种计算描述标量湍流脉动的截尾Gauss概率密度函数的待定参数的方法. 通过将关于待定参数的代数方程组表示成适于求解的形式，综合应用牛顿法、牛顿下山法和阻尼牛顿法等迭代算法，并恰当地选取待定参数的迭代初值，获得了在标量平均值及其脉动均方值的各种取值条件下待定参数的相应数值.     

Single-pulse chaotic dynamics of functionally graded materials plate

Single-pulse chaos are studied for a functionally graded materials rectangular plate. By means of the global perturbation method, explicit conditions for the existence of a Silnikov-type homoclinic orbit are obtained for this system, which suggests that chaos are likely to take place. Then, numerical simulations are given to test the analytical predictions. And from our analysis, when the chaotic motion occurs, there are a quasi-period motion in a two-dimensional subspace and chaos in another two-dimensional supplementary subspace.     

Nonlinear deformation analysis of a U-shaped bellows with varying thickness

Summary The nonlinear integral equations for a U-shaped bellows with compressed angle and varying wall-thickness are derived according to the simplified Reissner theory of large deflection for revolution shells and integral-equation method. The iteration procedure for nonlinear analysis is developed by means of the integral equation iteration in conjunction with the gradient method. Numerical solutions for a U-shaped bellows under the action of axial compression force and internal pressure are obtained, which are compared with previous theories and experiments. The present results are shown to have a good accuracy, and may be applied directly to the design of bellows. Received 13 November 1997; accepted for publication 6 July 1999