两自由度机械臂λ^2=1下的Hopf分岔与混沌研究

研究了一类周期系数力学系统因周期运动失稳而产生Hopf分岔及混沌问题.首先根据拉格朗日方程给出了该力学系统的运动微分方程,并确定其周期运动的具有周期系数的扰动运动微分方程,再根据Floquet理论建立了其给定周期运动的Poincaré映射,根据该系统的特征矩阵有一对复共轭特征值从-1处穿越单位圆情况,分析该Poincaré映射不动点失稳后将发生次谐分岔、Hopf分岔、倍周期分岔,而多次倍周期分岔将导致混沌.并用数值计算加以验证.结果表明,随着分岔参数的变化,系统的周期运动可通过次谐分岔形成周期2运动,进而发生Hopf分岔形成拟周期运动,并再次经次谐分岔、倍周期分岔形成混沌运动.     

Three-dimensional waves on the surface of a viscous fluid

The study of the effect of viscosity on the propagation of surface waves has traditionally been confined to the consideration of plane (two-dimensional) waves [1, 2]. So far the effect associated with taking the transverse modulation of the wave profile into account have not been studied. In what follows, a solution is constructed and analyzed for linear three-dimensional periodic waves in an infinitely deep fluid. Their distinguishing property is the presence of a vorticity in the direction of propagation. An expression for the average (over the wavelength) velocity of horizontal particle drift is found in the quadratic approximation in the small wave steepness.     

Effects of dynamic viscoelastic properties on acoustic diffraction by a solid sphere submerged in a viscous fluid

Summary  This study provides a general analysis for scattering of a planar monochromatic compressional sound wave by a homogeneous, isotropic, viscoelastic, solid sphere immersed in an unbounded viscous, heat-nonconducting, compressible fluid. The dynamic viscoelastic properties of the spherical scatterer and the viscosity of the surrounding fluid are rigorously taken into account in the solution of the acoustic-scattering problem. Havriliak–Negami model for viscoelastic material behaviour along with the appropriate wave-harmonic field expansions and the pertinent boundary conditions are employed to develop a closed-form solution in form of infinite series. Subsequently, the associated acoustic quantities such as the scattered far-field pressure directivity pattern, scattered intensity distribution, differential scattering cross section, and the acoustic radiation force are evaluated for given sets of viscoelastic material properties. Numerical results clearly indicate that, in addition to the traditional fluid viscosity-related mechanisms, the dynamic viscoelastic properties of the solid obstacle can be of major significance in sound scattering. Limiting cases are examined and fair agreements with well-known solutions are established. Received 15 January 2002; accepted for publication 2 July 2002 The authors wish to sincerely thank professors Daniel Levesque, Roderic Lakes, Yves Berthelot, S. Temkin, and Andrei Dukhin for valuable and productive consultations on dynamic theory of viscoelasticity and acoustics of (thermo)viscous media.     

On the Relation between Fronts and High-Shear Layers in Wall Turbulence

Direct numerical simulation results of turbulent channel flow are analyzed in order to examine the relation between two kinds of near-wall flow structures, namely the instantaneous shear layers and the fronts which are derived from two-point statistics of the streamwise velocity component. The near-wall shear layers are analyzed by flow visualizations and conditional sampling, while the fronts are examined by means of space-time correlations and spatial two-point correlation functions. The present study focuses on the analysis of the propagation speed and the spatial shape of the structures. Concerning the propagation speed it is shown that the results obtained from flow visualizations are in close agreement with the propagation velocities derived from space-time correlation functions. The comparison of VISA results for the instantaneous shear with spatial structures obtained from two-point correlations of the streamwise velocity and the shear gives evidence that the fronts are intimately related to the pronounced near-wall shear layers.     

The general properties of the spherical vortices (SV) ofn-TH order and the chaotic phenomena and of the ordered structures of the SV of 3RD order

The general properties of the spherical vortices (SV) of n-th order are discussed in this paper. Numerical calculations are carried out in the case of n=3. We find out some interesting phenomena concerning the chaotic regions and ordered islands on the Poincaré sections. Interpretations of these phenomena are also given. Project supported by the National Basic Research (Nonlinear Science) Foundation of China     

Rayleigh-Marangoni-Benard instability in two-layer fluid system

Rayleigh-Marangoni-Bénard instability in a system of two-layer fluids is studied numerically. The convective instabilities in the system of Silicon Oil (10cSt) and Fluorinert (FC70) liquids have been analyzed. The critical parameters at onset of convection are presented in a large range of two-layer depth ratios from 0.2 to 5.0. Numerical results show that the instability of the two-layer system depends strongly on its depth ratio. When the depth ratio increases, the instability mode changes from mechanical coupling to thermal coupling. Between these two typical coupling modes, a time-dependent oscillation is detected. Nevertheless, traveling wave states are found in the case of oscillatory instability. The oscillation mode results from the competition between Rayleigh instability and Marangoni effect. The project supported by the National Natural Science Foundation of China (10372105) and the Knowledge Innovation Program of Chinese Academy of Sciences (KJCX2-SW-L05)     

The study on the chaotic motion of a nonlinear dynamic system

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The double mode model of the chaotic motion for a large deflection plate

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数值流形方法的粘性边界问题初探

在实际工程数值流形方法分析中,采用固定约束边界的方法处理无限域或者半无限域的情况,边界处应力波的反射造成模拟结果与实际情况不符.本文基于Lysmer等人提出的粘性边界理论,在边界上设置阻尼器,推导相应粘性边界条件下流形单元刚度矩阵的数值计算格式,经岩石长条中弹性波传播算例,并与有限元结果对比,验证了该粘性边界的有效性,有利于数值流形方法的工程中推广应用.     

Numerical simulation of plate autorotation in a viscous fluid flow

A general formulation of the plane coupled dynamical and aerodynamical problem of the motion of a rigid body with a rotational degree of freedom in a viscous incompressible fluid flow is given. A computation technique for solving the Navier-Stokes equations based on the meshless viscous vortex domain method is used. The autorotation of a single plate and a pair of plates is investigated. The effect of the reduced moment of inertia and the Reynolds number on the angular rotation velocity is determined. The time dependences of the hydrodynamic loads are compared with the corresponding instantaneous flow patterns. The increased the autorotation velocity of two plates in tandem is detected.