保持顶点多样性的复合形法及其在边坡稳定分析中的应用

针对基本复合形法全局搜索能力不强的缺陷,改进了基本复合形法的寻优方法。在关于各个顶点的寻优直线上分别找出比各个顶点优异的点并替换掉各顶点构成多个新复形,并以各个复合形中心点到各个顶点的海明距离之和为中心距指标,找出最大中心距的复形为下一次迭代之新复形。依次迭代,直到没有新的复形产生。通过对两个复杂边坡最小安全系数的搜索,发现本文新复合形法的全局搜索能力有较大提高。     

Lag synchronization of hyperchaotic complex nonlinear systems

In this paper, we study the lag synchronization (LS) of n-dimensional hyperchaotic complex nonlinear systems. The idea of the nonlinear control technique based on the complex Lyapunov function with lag in time is used to propose a scheme to investigate LS of hyperchaotic attractors of these systems. Both complex Lyapunov and control functions are introduced. For illustration, the scheme is applied to two hyperchaotic complex Lorenz systems. The real and complex control functions are derived analytically to achieve LS and to show that the complex error dynamical systems are globally stable. Numerical results are calculated to test the validity of the analytical expressions of control functions to achieve LS of two identical hyperchaotic attractors.     

Complex modified projective synchronization of two chaotic complex nonlinear systems

In this paper, we present a novel type of synchronization called complex modified projective synchronization (CMPS) and study it to a system of two chaotic complex nonlinear 3-dimensional flows, possessing chaotic attractors. Based on the Lyapunov function approach, a scheme is designed to achieve CMPS for such pairs of (either identical or different) complex systems. Analytical expressions for the complex control functions are derived using this scheme to achieve CMPS. This type of complex synchronization is considered as a generalization of several kinds of synchronization that have appeared in the recent literature. The master and slave chaotic complex systems achieved CMPS can be synchronized through the use of a complex scale matrix. The effectiveness of the obtained results is illustrated by a studying two examples of such coupled chaotic attractors in the complex domain. Numerical results are plotted to show the rapid convergence of modulus errors to zero, thus demonstrating that CMPS is efficiently achieved.     

Smoothing Identification of Systems with Small Non-linearities

This paper deals with simplified mathematical models of the dynamic systems with weak non-linearities and described by complex continuous transfer functions without jumping. We consider only the first approximation of the steady state forced vibration where the complex amplitude corresponds to the same frequency as the harmonic excitation. The iterative smoothing of the above system from the measured transfer function at discrete frequency points and especially from their moduli is proposed. The aim of this method is to determine the complex eigenvalues of the systems with Duffing-type stiffness behaviour (only their imaginary parts depend on the squares of the absolute values of the amplitudes) and real modal parameters in situations when no-phase difference between output and input is known. If the complex transfer function is completely known, the identified complex eigenvalues are assumed to be linear and quadratic functions of absolute values of amplitudes and the modal parameters are complex.     

Adaptive generalized function projective synchronization of uncertain chaotic complex systems

The complex nonlinear systems appear in many important fields of physics and engineering, which are very useful for cryptography and secure communication. This paper investigates adaptive generalized function projective synchronization (AGFPS) between two different dimensional chaotic complex systems with fully or partially unknown parameters via both reduced order and increased order. Based on the Lyapunov stability theorem and adaptive control technique, a general adaptive controller with corresponding parameter update rule is constructed to achieve AGFPS between two nonidentical chaotic complex systems with distinct orders, and identify the unknown parameters simultaneously. This scheme is then applied to obtain AGFPS between the hyperchaotic complex Lü system and the chaotic complex Lorenz system with fully unknown parameters, and between the uncertain chaotic complex Chen system and the uncertain hyperchaotic complex Lorenz system, respectively. Corresponding simulations results are performed to show the feasibility and effectiveness of the proposed synchronization method.     

The use of complex valued functions for the solution of three-dimensional elasticity problems

For the treatment of plane elasticity problems the use of complex functions has turned out to be an elegant and effective method. The complex formulation of stresses and displacements resulted from the introduction of a real stress function which has to satisfy the 2-dimensional biharmonic equation. It can be expressed therefore with the aid of complex functions. In this paper the fundamental idea of characterizing the elasticity problem in the case of zero body forces by a biharmonic stress function represented by complex valued functions is extended to 3-dimensional problems. The complex formulas are derived in such a way that the Muskhelishvili formulation for plane strain is included as a special case. As in the plane case, arbitrary complex valued functions can be used to ensure the satisfaction of the governing equations. Within the solution of an analytical example some advantages of the presented method are illustrated.     

Libration points of a rotating complexified triangle

Similarities and differences between the force fields of a classical real dipole and a complex dipole are analyzed. The complex dipole is a pair of points equipped with complex conjugate masses and situated in a complex domain. The results of this analysis are used in the problem of motion of a material point in the field of attraction of a triangle uniformly rotating in its plane about its center of mass. It is assumed that a complex dipole is assigned to each vertex of the triangle. The existence and stability of libration points are studied. In particular, it is shown that there exist libration points outside the plane of the triangle.     

On the two basic problems of complex damping theory

In this paper, two important basic problems relating to the complex damping theory are discussed. The two problems are: (1) the essence of complex damping, and (2) the dynamic solution of structures with complex damping in time domain. To investigate the above problems, the frequency-dependent viscous damping theory is established and the correct and applicable solution of forced vibration for a complex damping oscillator is given beforehand.Supported by the Joint Earthquake Foundation     

Complex function projective synchronization of complex chaotic system and its applications in secure communication

To develop secure communication, the paper presents complex function projective synchronization (CFPS) of complex chaotic systems. Aimed to coupled complex chaotic system, the control law is derived to make the complex state vectors asymptotically synchronize up to a desired complex function matrix. Based on CFPS, a novel communication scheme is further designed in theory. Its main idea is chaotic masking in essence, but the transmitted signal is the derivative of the product of the information signal and chaotic signal. As the complex scaling functions are arbitrary and more unpredictable than real scaling functions, and the product and derivative operations of complex numbers are complicated, the possibility that an interceptor extracts the information from the transmitted signal is greatly reduced. The communication system can transmit analog signal and digital symbols with fast transmission and high security, especially low bit-error rate and the strong robustness to noise for digital symbols. The corresponding numerical simulations are performed to verify and illustrate the analytical results.     

不同类型地震波作用下地下综合体结构地震反应分析

为探究不同类型地震波作用下地下综合体结构的地震反应特征,本文以上海某地下综合体为工程背景,采用ABAQUS软件建立土-地下综合体结构相互作用体系三维有限元模型,利用Davidenkov模型模拟土的非线性,以不同类型的单向地震波和双向地震波（含水平向和竖向）作为输入,对软土场地中地下综合体结构进行了地震反应分析,比较了不同类型地震波作用下地下综合体结构地震反应的差异,探讨了地下综合体结构的竖向地震动效应问题．本文的算例结果表明：在长周期地震波作用下地下综合体结构的位移响应和内力响应峰值均明显大于普通地震波作用下的结果;考虑竖向地震动时地下综合体结构的柱轴力较单一水平向地震动作用情形有明显增大;在本文地下综合体结构算例中,地下三层柱底、四层柱顶、五层柱底、以及底板与侧墙连接处为受力较大部位．     

On the representation of three-dimensional elasticity solutions with the aid of complex valued functions

In this paper the representation of three-dimensional displacement fields in linear elasticity in terms of six complex valued functions is considered. The representation includes the complex Muskhelishvili formulation for plane strain as a special case. The completeness of the complex representation for regular solutions is shown and a relationship to the Neuber/Papkovich solutions is given.     

多烷基环戊烷制备复合磺酸钙基润滑脂及其摩擦学性能研究

以多烷基环戊烷(MACs)为基础油制备了复合磺酸钙基润滑脂,研究了液态高分子量酚类抗氧剂(L135)、苯三唑衍生物(T551)和噻二唑类衍生物(T561)对复合磺酸钙基润滑脂性能的影响,采用热重分析(TGA)仪评价了润滑脂的热稳定性;利用往复摩擦磨损试验机(MFT-R4000)分析了L135、T551和T561在钢/钢摩擦副下对复合磺酸钙基润滑脂摩擦磨损性能的影响,利用扫描电子显微镜(SEM)和能谱仪(EDS)对磨损表面进行了分析.结果表明:以MACs为基础油制备的复合磺酸钙脂具有优良的热稳定性能;同时MACs复合磺酸钙脂与3种添加剂具有良好的相容性能,表现在MACs复合磺酸钙脂具有更好的减摩抗磨性能,其原因归结为MACs在摩擦副表面形成较为牢固的物理吸附膜和含S、N和Fe等生成的化学反应膜.     

Robust adaptive full state hybrid synchronization of chaotic complex systems with unknown parameters and external disturbances

This paper studies the robust adaptive full state hybrid projective synchronization (FSHPS) scheme for a class of chaotic complex systems with uncertain parameters and external disturbances. By introducing a compensator and using nonlinear control and adaptive control, the robust adaptive FSHPS scheme is derived, which can eliminate the influence of uncertainties effectively and achieve adaptive FSHPS of the chaotic (hyperchaotic) complex systems asymptotically with a small error bound. The adaptive laws of the unknown parameters are given, and the sufficient conditions of realizing FSHPS are derived as well. Moreover, we also discuss the case that parameters of chaotic complex system are complex. Finally, the complex Chen system and Lü system, and the hyperchaotic complex Lorenz system are taken as two examples and the numerical simulations are provided to verify the effectiveness and robustness of the proposed control scheme.     

Analysis of nonlinear chaotic vibrations of shallow shells of revolution by using the wavelet transform

In the present paper, we study complex vibrations of flexible axisymmetric shallow shells under the action of transverse sing-alternating pressure. In addition to the traditional methods of nonlinear dynamics, we for the first time use the wavelet transform to analyze the transition from harmonic to chaotic vibrations. We analyze the use of Gauss-type wavelets (the order of derivatives varies from m = 1 to m = 8) and also the use of the Morlet wavelet (both real and complex). We conclude that the use of the complex Morlet wavelet is preferable to that of the Gaussian wavelets: the more zero moments a wavelet has, the better it describes the complex vibrations of flexible shallow shells.     

基于复数神经网络的粘弹性材料动态模量拟合方法

固体火箭发动机药柱粘弹性材料除具有弹塑性特性,还具有粘滞性,这一特性使得材料变形具有明显的时间效应,本构关系复杂,进行动态力学分析时,动态模量难以有效拟合．本文提出了一种基于(Levenberg-Marquardt, L-M)算法的复数神经网络拟合粘弹性材料动态模量的方法．通过广义Maxwell模型推导得到材料的动态模量表达式,以此构造未定网络参数为复数的神经网络,从而提供了一种输入、输出样本均为复数的神经网络解决方法．将实数L-M训练算法进行改进,衍生到复数领域,提出复数L-M训练算法．通过粘弹性材料实验,将实验数据时温等效转换,获得复数神经网络的训练及测试样本．通过对神经网络进行训练,实现粘弹性材料动态模量的高精度拟合．数值算例表明,与传统神经网络拟合方法相比,所提方法在训练速度和泛化能力方面都有其优越性．     

Parameter identification and adaptive impulsive synchronization of uncertain complex-variable chaotic systems

Synchronization of nonlinear dynamical systems with complex variables has attracted much more attention in various fields of science and engineering. In this paper, the problem of parameter identification and adaptive impulsive synchronization for a class of chaotic (hyperchaotic) complex nonlinear systems with uncertain parameters is investigated. Based on the theories of adaptive control and impulsive control, a synchronization scheme is designed to make a class of chaotic and hyperchaotic complex systems asymptotically synchronized, and uncertain parameters are identified simultaneously in the process of synchronization. Particularly, the proposed adaptive–impulsive control laws for synchronization are simple and can be readily applied in practical applications. The synchronization of two identical chaotic complex Chen systems and two identical hyperchaotic complex Lü systems are taken as two examples to verify the feasibility and effectiveness of the proposed controllers and identifiers.     

A simulation of the cascading failure of a complex network model by considering the characteristics of road traffic conditions

Using the dual method, we start with a traditional road traffic network with a constructed logic network with small-world characteristics and construct the complex network of road traffic. After analyzing and comparing with other complex networks, the time delay, restorative, and other characteristics are presented for the complex network of road traffic, and then, the cascading failure model of the complex network is simulated. The simulation results show that using different time delays, an incident dissipation factor and load capacity can reasonably avoid a cascading failure, and they can remove its effects. In addition, our results provide value and guidance for building a road traffic network that prevents and removes the cascading failure of a road network.

     

Analysis of structurally complex nanocomposites (review)

Structurally complex nanocomposites (their fillers have complex shape, which complicates the theoretical analysis of these composites) are considered. Nanotubes of quite complex shape that are very difficult to theoretically describe and analyze are exemplified. Fibrous and particulate composites reinforced with bristled nanofibers and bristled knedel-like nanogranules, respectively, are described and analyzed theoretically. Theoretical approaches to studying nanocomposites with large-scale and small-scale bendings of nanotubes are outlined