Nonlinear Normal Modes of Buckled Beams: Three-to-One and One-to-One Internal Resonances

Nonlinear normal modes of a fixed-fixed buckled beam about its first post-buckling configuration are investigated. The cases of three-to-one and one-to-one internal resonances are analyzed. Approximate solutions for the nonlinear normal modes are computed by applying the method of multiple scales directly to the governing integral-partial-differential equation and associated boundary conditions. Curves displaying variation of the amplitude of one of the modes with the internal-resonance-detuning parameter are generated. It is shown that, for a three-to-one internal resonance between the first and third modes, the beam may possess one stable uncoupled mode (high-frequency mode) and either (a) one stable coupled mode, (b) three stable coupled modes, or (c) two stable and one unstable coupled modes. For the same resonance, the beam possesses one degenerate mode (with a multiplicity of two) and two stable and one unstable coupled modes. On the other hand, for a one-to-one internal resonance between the first and second modes, the beam possesses (a) two stable uncoupled modes and two stable and two unstable coupled modes; (b) one stable and one unstable uncoupled modes and two stable and two unstable coupled modes; and (c) two stable uncoupled and two unstable coupled modes (with a multiplicity of two). For a one-to-one internal resonance between the third and fourth modes, the beam possesses (a) two stable uncoupled modes and four stable coupled modes; (b) one stable and one unstable uncoupled modes and four stable coupled modes; (c) two unstable uncoupled modes and four stable coupled modes; and (d) two stable uncoupled modes and two stable coupled modes (each with a multiplicity of two).     

二维联合概率分布函数构造方法对结构串联系统可靠度影响分析

简要介绍了两种构造联合分布函数近似方法：基于Pearson相关系数的近似方法P和基于Spearman相关系数的近似方法S。推导了基于直接积分方法的串联系统失效概率计算公式,提出了两构件功能函数间负相关时串联结构系统失效概率上限值的计算公式。以理论联合概率分布函数是二维极值分布为例研究了两种近似方法在串联系统可靠度计算中的精度。结果表明,两种近似方法能够有效地计算串联结构系统可靠度,且精度很高,为不完备概率信息条件下串联结构系统可靠度分析提供了一条有效的途径。当两构件的功能函数正相关时,两种近似方法误差随串联系统失效概率的减小而增加,但近似方法与精确方法系统失效概率的差别最大也不会超过2倍;当两构件的功能函数负相关时,两种近似方法误差随系统失效概率的减小而减小,但两种近似方法的失效概率几乎与精确解一样。此外,两种近似方法误差不是随构件间相关性的增加而单调增加,而是存在一极大值。     

统一二阶矩模型用于模拟旋流湍流两相流动

用统一二阶矩模型（ＵＳＭ）模拟了旋流数为０４７和１５的气粒两相流动，并和实验结果以及ｋ ε ｋｐ模型的模拟结果进行了对比．研究结果表明，提高旋流数减小了轴向速度反流区，增大了切向速度似固核区．ＵＳＭ和ｋ ε ｋｐ模型预报旋流数为０４７时的两相速度场差别不大，并都和实验结果接近，但前者预报的旋流数为１５的两相速度场比后者有改进，在两种情况下，前者都能揭示出后者无法预报的两相湍流各向异性规律．     

The global analysis of higher order nonlinear dynamical systems and the application of cell-to-cell mapping method

In this paper, the general characteristics and the topological consideration of the global behaviors of higher order nonlinear dynamical systems and the characteristics of the application of cell-to-cell mapping method in this analysis are expounded. Specifically, the global analysis of a system of two weakly coupled van der Pol oscillators using cell-to-cell mapping method is presented.The analysis shows that for this system, there exist two stable limit cycles in 4-dimensional state space, and the whole 4-dimensional state space is divided into two almost equal parts which are, respectively, the two asymototically stable domains of attraction of the two periodic motions of the two stable limit cycles. The validities of these conclusions about the global behaviors are also verified by direct long term numerical integration. Thus, it can be seen that the cell-to-cell mapping method for global analysis of fourth order nonlinear dynamical systems is quite effective.     

Numerical Simulation of Aerodynamic Characteristics of Two Rectangular Cylinders in Side-by-side Arrangement

We present numerical results of flows around two rectangular cylinders in side-by-side arrangement by three-dimensional computations. The two rectangular cylinders are arranged with various distances between the cylinders. The three-dimensional flow structures around two rectangular cylinders denote significant features depending on the distance between the cylinders. In our computations, the Reynolds number Re is set as 10,000, and both the aspect ratio of section of two rectangular cylinders and the distance between the cylinders are considered as parameters to calculate the flow around two rectangular cylinders. The obtained numerical results are also compared with experimental data.     

A numerical study on the flow patterns of two oscillating cylinders

Flow around two oscillating cylinders in a side-by-side arrangement at Reynolds number (Re)=185 is simulated using the immersed boundary method. The purpose of this study is to investigate the combined effects of the gap between the two cylinders and their oscillation in the flow. The cylinders oscillate transversely to a uniform cross-flow with a prescribed sinusoidal function in the opposite direction, with the oscillation amplitude equal to 20% of the cylinder diameter. The gap between the two cylinders and the oscillating frequency are chosen as major variables for the parametric study to investigate their influence on the flow pattern. The ratio of mean gap distance between the two oscillating cylinders to the cylinder diameter is chosen to be 0.6, 1.0, 1.4, and 1.8, and the ratio of oscillating frequencies to the natural vortex shedding frequency of a fixed cylinder is 0.8, 1.0, and 1.2. Wake patterns and the drag and lift coefficients are described and compared with those from a single oscillating cylinder and two stationary cylinders. The wake patterns of two oscillating cylinders can be explained by flow mechanisms of two stationary cylinders, a single oscillating cylinder, and their combinations, and are in agreement with classifications of flow over two stationary cylinders presented in previous studies. In the case of two oscillating cylinders, the modulation phenomenon appears from a lower excitation frequency than in a single oscillating cylinder. Generally, oscillating cylinders have higher drag and root-mean-square (r.m.s.) values of drag coefficients than stationary cylinders.     

Soliton solutions for the reduced Maxwell–Bloch system in nonlinear optics via the N-fold Darboux transformation

Under investigation in this paper is the reduced Maxwell?CBloch system, which describes the propagation of the intense ultra-short optical pulses through a two-level dielectric medium. Through symbolic computation, conservation laws are derived and N-fold Darboux transformation (DT) is constructed for that system. By virtue of the DT obtained, multi-soliton solutions are generated. Figures are plotted to reveal the following dynamic features of the solitons: (1) Elastic interactions between two bright one-peak solitons, between two bight two-peak solitons and between two dark two-peak solitons; (2) Parallel propagations between two bright one-peak solitons, between two bright two-peak solitons and between two dark two-peak solitons; (3) Periodic propagations of hump solitons, of a pair of bound hump solitons with the same amplitude and of dark solitons.     

Third-Order Upwind Finite Element Simulation of Flow Around Two Square Cylinders

The aerodynamic behavior of the flow around two square cylinders is presented on the basis of the numerical simulation of the incompressible Navier-Stokes equations using a third-order upwind finite element scheme. It is well known that flow patterns around the two square cylinders are more complicated than flow patterns around one square cylinder because of interference between the Karman vortices behind the two square cylinders. In this paper, two kinds of cylinder arrangements are chosen as computational models. One type is that of two square cylinders arranged vertically to the direction of a uniform flow, and the other is arranged horizontally to the direction of a uniform flow.     

随机神经网络优化方法及其计算机仿真

研究了结构优化问题求解的随机神经网络方法,可较好地克服Hopfield网络方法容量陷入局部解的缺点,针对实例,对随机神经网络和Hopfield网络进行了动态仿真,直观地给出了两种网络的动态并行运行,能量函数的动态变化过程及两种网络的全局性的差异,同时也仿真出了网络并行运行至稳定优化解的时间。     

The general variational principle of the cantilever beam of circular cross section including transverse shear deformation

In this paper we derive the approximate theory on the straight cantilever beam of a same circular cross section including transverse shear deformation, using the general variational principle with two class variates, and we present the expression with two class variates containing two general displacement, of general complementary energy, corresponding with the theory.     

Holographic moiré for strain fringe patterns

New holographic-moiré methods are presented to obtain strain fringe patterns. To introduce two carriers of different directions, two kinds of recording procedures are proposed: (1) triple-exposure recording by two object beams and one reference beam (all of these beams are identical in polarization state) and (2) double exposure or real-time recording by two orthogonally polarized object beams and two corresponding reference beams. In these recordings, the carriers are introduced by changing the directions of the reference beams and are modulated by deformation. Separated in-plane displacement derivative patterns are then obtained by optical processings. Both the principles and the experimental results are shown in the paper.     

Scalar interactions between parallel jets measured using a two-channel PLIF technique

A two-channel PLIF technique that simultaneously quantifies two scalar fields is presented. The technique consists of two independently operated single-color PLIF systems that synchronously image a common region. Two dyes (fluorescein sodium salt and oxazine 725) are excited by two lasers (argon-ion and krypton-ion), and the resulting fluorescence is imaged by a pair of cameras. The two-channel system is used to study mixing between two parallel jets, each transporting a different scalar species. Time-averaged and instantaneous mixing statistics are calculated and used to show the effects of turbulent structure on scalar mixing. In particular, the existence of positive spatial correlations between the two scalar fields is demonstrated in off-axis mixing regions.     

两级分块结构化网格在SK型静态混合器中的应用

给出一种适用于SK型静态混合器流场数值模拟的两级分块结构化网格划分方案和分块圆弧区点的极坐标方程。与常用的非结构四面体网格划分对比,两种方法划分网格数量相近时,两级分块结构化网格达到的迭代精度高于非结构化网格一个等级,而非结构化网格收敛所用时间约为结构化网格收敛所用时间的1.25倍;运用控制体积容积变化值对两种方法划分网格进行质量评估,结构化网格划分方法接近99%网格质量指标在1.0~2.0范围内,而非结构化网格仅接近60%网格质量指标在1.0~2.0范围内。通过实验测量对两种方法划分网格数值模拟结果进行对比验证,结构化网格计算结果与实验值更为接近,表明其可行性和准确性均优于非结构四面体网格划分。     

General exact solution of incompressible potential flows around two circles

Three exact solutions are obtained for 2-D incompressible potential flows around two moving circles in three cases: (i) expansion (or contraction) of themselves, (ii) approaching (or departing from) each other, (iii) moving perpendicularly to the line connecting the centres in opposite directions. Meanwhile, another set of two exact solutions is obtained for 2-D incompressible potential flows between two moving eccentric circles in two cases: moving parallely or perpendicularly to the line connecting the centres.     

Original ArticleKinematic hardening rules in finite plasticity Part II: Some examples

We consider finite plasticity laws which are represented by means of dual variables and satisfy the intrinsic dissipation inequality. Within two families of dual variables, two different formulations for a kinematic hardening rule, referred to as Model 1 and Model 2, are proposed. In order to discuss basic properties of the two models, the predicted response for some simple deformations is calculated. It turns out that e.g. with respect to the simple shear and simple torsion the two models differ mainly in the effects of second order. Received June 14, 1995     

Generalized variational principles for boundary value problem of electromagnetic field in electrodynamics

An expression of the generalized principle of virtual work for the boundary value problem of the linear and anisotropic electromagnetic field is given. Using Chien＇s method, a pair of generalized variational principles （GVPs） are established, which directly leads to all four Maxwell＇s equations, two intensity-potential equations, two constitutive equations, and eight boundary conditions. A family of constrained variational principles is derived sequentially. As additional verifications, two degenerated forms are obtained, equivalent to two known variational principles. Two modified GVPs are given to provide the hybrid finite element models for the present problem.     

Nonlinear dynamics of two harmonic oscillators coupled by Rayleigh type self-exciting force

The present paper reports some interesting phenomena observed in the nonlinear dynamics of two self-excitedly coupled harmonic oscillators. The system under consideration consists of two mechanical oscillators coupled by the Rayleigh type self-exciting force. Both autonomous and nonautonomous cases for weakly coupled systems are analyzed. When the natural frequencies of the two oscillators are close to each other, only one mode of oscillation exists. As two modes of oscillations get locked to a single mode, the system is said to be in a mode-locked condition. Under a mode-locked condition, the oscillators can oscillate with only a single frequency. However, when two oscillators are sufficiently detuned, the mode-locking condition does not persist and two distinct modes of oscillations emerge. Under these circumstances, particularly when detuning is large, one of the oscillators, depending on the initial conditions, oscillates with much larger amplitude as compared to the other oscillator, and hence mode localization is observed. When one of the oscillators is subject to a harmonic excitation, at two different frequencies, termed here as the decoupling frequencies, the coupling between the oscillators is almost lost, resulting in almost zero response of the unexcited oscillator. Analytical and numerical results are presented to analyze the above mentioned phenomena. Some potential applications of the aforesaid phenomena are also discussed.     

一端弹性支撑的串列双柱和并列双柱在气流中自由端的振幅响应

本文研究了一端弹性支撑的并列双柱和串列双圆柱在气流中自由端的振幅响应，与单圆柱相比，在小间距时，串列双圆柱中前柱的横向振幅受到较强的激励。而在大间距时，振幅受到抑制，特别当Ｌ／Ｄ＝３．５和４．０时，其振幅响应仅为单柱的１／３左右，而对于后柱，则在大间距时，纵向振幅响应有所增大，而且后柱的振幅响应要比前柱的大得多，而并列双圆柱的自由端振幅基本上受到抑制，在Ｔ／Ｄ＞３．０之后，干扰很快减小到接近单个圆     

双圆诱导不可压缩势流的几个精确解

Lagally(1929)给出了两个静止圆在均匀来流中的扰动速度势精确解。本文通过使用 Apollonius 保角变换,将两圆外部区域变为圆环内部区域,并在变换平面上用 Fo-urier 级数方法求解 Laplace 方程,从而得出双圆扰动势流的另外三个精确解。它们分别对应于静止流体中两圆膨胀(收缩)、沿连心线相向(相背)运动和垂直连心线反向运动(错动)所诱导的速势场。     

High‐resolution,monotone solution of the adjoint shallow‐water equations

A monotone, second‐order accurate numerical scheme is presented for solving the differential form of the adjoint shallow‐water equations in generalized two‐dimensional coordinates. Fluctuation‐splitting is utilized to achieve a high‐resolution solution of the equations in primitive form. One‐step and two‐step schemes are presented and shown to achieve solutions of similarly high accuracy in one dimension. However, the two‐step method is shown to yield more accurate solutions to problems in which unsteady wave speeds are present. In two dimensions, the two‐step scheme is tested in the context of two parameter identification problems, and it is shown to accurately transmit the information needed to identify unknown forcing parameters based on measurements of the system response. The first problem involves the identification of an upstream flood hydrograph based on downstream depth measurements. The second problem involves the identification of a long wave state in the far‐field based on near‐field depth measurements. Copyright © 2002 John Wiley & Sons, Ltd.