Bifurcation characteristics analysis of a class of nonlinear dynamical systems based on singularity theory

A method for seeking main bifurcation parameters of a class of nonlinear dynamical systems is proposed. The method is based on the effects of parametric variation of dynamical systems on eigenvalues of the Frechet matrix. The singularity theory is used to study the engineering unfolding(EU) and the universal unfolding(UU) of an arch structure model, respectively. Unfolding parameters of EU are combination of concerned physical parameters in actual engineering, and equivalence of unfolding parameters and physical parameters is verified. Transient sets and bifurcation behaviors of EU and UU are compared to illustrate that EU can reflect main bifurcation characteristics of nonlinear systems in engineering. The results improve the understanding and the scope of applicability of EU in actual engineering systems when UU is difficult to be obtained.     

论工程优化

本文首先讨论了土建工程设计问题的软科学性质和这些问题中所包含的不确定性（随机性、模糊性和未确知性）信息及其科学处理；然后简要地介绍了作者所提出的工程大系统的全局优化和结构的不确定性优化设计的理论和方法；最后讨论了工程软科学所应包含的各种问题。     

时滞系统动力学近期研究进展与展望

综述了1999年以来时滞系统动力学在力学、机械工程、航空航天、生态学、生物学、神经网络、激光、电子和信息技术、保密通讯和经济学等领域的研究进展, 总结了其中的研究方法. 通过本文可以看出时滞系统普遍存在于自然和工程实际中, 即使对已经非常熟悉的简单振子,考虑到时滞的影响, 仍有许多问题有待作更深入的理论研究和新现象的发现.针对以往研究中出现的问题, 提出今后几年的发展方向、建议和展望, 同时指出了在理论上急需解决的一些科学问题,例如以时滞反馈控制为中心的控制策略、非线性因素和时滞联合作用的影响、时滞导致的多级分岔使系统呈现出复杂动力学行为、以时滞状态变量耦合为中心构成的网络系统计算模型对系统的影响等问题都是非线性动力学系统所遇到的科学基础问题.      

Stability of Singularly Perturbed Systems with Structural Perturbations. General Theory

Singularly perturbed systems with structural perturbations are analyzed for stability. New sufficient conditions of asymptotic stability and uniform asymptotic stability are established. The systems in question are widely used in control theory, engineering, etc     

Transmissibility of non-linear output frequency response functions with application in detection and location of damage in MDOF structural systems

Transmissibility is a well-known linear system concept that has been widely applied in the diagnosis of damage in various engineering structural systems. However, in engineering practice, structural systems can behave non-linearly due to certain kinds of damage such as, e.g., breathing cracks. In the present study, the concept of transmissibility is extended to the non-linear case by introducing the Transmissibility of Non-linear Output Frequency Response Functions (NOFRFs). The NOFRFs are a concept recently proposed by the authors for the analysis of non-linear systems in the frequency domain. A NOFRF transmissibility-based technique is then developed for the detection and location of both linear and non-linear damage in MDOF structural systems. Numerical simulation results verify the effectiveness of the new technique. Experimental studies on a three-storey building structure demonstrate the potential to apply the developed technique to the detection and location of damage in practical MDOF engineering structures.     

多柔体系统动力学建模与优化研究进展

多柔体系统是由柔性部件和运动副组成的力学系统,在航空、航天、车辆、机械与兵器等众多工程领域具有广泛的应用前景, 其典型的代表包括柔性机械臂、直升机旋翼、卫星的可展开天线、太阳帆航天器等. 近年来,随着工程技术的发展,多柔体系统动力学问题日益突出,尤其是含变长度柔性部件的多柔体系统,不仅涉及其动力学 建模与计算,还涉及其动力学优化设计. 事实上,部件柔性对多柔体系统的动力学行为影响很大,直接影响到优化结果,因此需要发展基于多柔体系统动力学的优化设计方法. 本文首先阐述了多柔体系统动力学优化的研究背景及意义,简要回顾了多柔体系统动力学建模的3类方法:浮动坐标方法、几何 精确方法和绝对节点坐标方法,并介绍了含变长度柔性部件的多柔体系统动力学建模方法. 系统概述了多柔体系统动力学响应优化、动力学特性优化和动力学灵敏度分析3个方面的研究进展,并从尺寸优化、形状优化和 拓扑优化 3 个方面综述了多柔体系统部件优化的研究进展. 本文最后提出了在多柔体系统动力学优化研究中值得关注的若干问题.      

Non-linear output frequency response functions of MDOF systems with multiple non-linear components

In engineering practice, most mechanical and structural systems are modelled as multi-degree-of-freedom (MDOF) systems such as, e.g., the periodic structures. When some components within the systems have non-linear characteristics, the whole system will behave non-linearly. The concept of non-linear output frequency response functions (NOFRFs) was proposed by the authors recently and provides a simple way to investigate non-linear systems in the frequency domain. The present study is concerned with investigating the inherent relationships between the NOFRFs for any two masses of non-linear MDOF systems with multiple non-linear components. The results reveal very important properties of the non-linear systems. These properties clearly indicate how the system linear characteristic parameters govern the propagation of the non-linear effect induced by non-linear components in the system. One potential application of the results is to detect and locate faults in engineering structures which make the structures behave non-linearly.     

生物结构自适应性的力学研究及其应用

以生物的骨组织、竹子以及植物根系、动物血管等生物分枝系统为例, 从微观组织结构和宏观形态, 以力学的观点, 对生物形态组织结构的自适应性进行了分析研究, 并概括地介绍了这种自适应性在工程材料及工程结构设计中的应用, 如基于骨组织重建机理的自修复材料、基于生物分枝系统形态生成机理的薄板加强筋以及热传递系统中散热通道的分布设计等. 模拟生物结构和系统的工程材料和结构及其设计方法, 因具有与生物结构和系统相似的优越性能, 可突破传统产品和设计方法的一些局限性. 基于仿生技术的生物形态、材料与机能、强度等关系的进一步研究, 以及相关的理想工程材料和结构的设计与制造方法的研究, 将是当前和未来十分重要的研究课题.      

Bridging reductionism and holism — multi-scale methodology with applications to particle-fluid systems

While science continues to extend to two extremes — micro-scale towards dimensions even smaller than elemental particles and mega-scale even beyond the universe, one recognizes that reductionism is not sufficient to solve many problems we encounter in engineering, which are likely characterized by nonlinearity, nonequilibrium and dissipative multi-scale structures. On the other hand, the common features of these nonlinear systems, such as bifurcation, state multiplicity and self-organization, have attracted much attention, leading to the approaches of the so-called complexity science which has become a focus not only in natural science and engineering science, but also in social science.However, no effective methodology has been established to understand these complex systems, though noticeable progress has been achieved in studying these systems, such as particle-fluid multi-phase systems. Multi-scale methodology has been considered as a promising methodology to tackle complex systems due to its capability in correlating phenomena at different scales. In this presentation, we shall review the development of the multi-scale methodology and its applications to particle-fluid systems, elucidating the essential relevance of complex systems and the challenging problems in chemical engineering.Multi-scale structure is considered to be the focus in studying complex systems, particularly, correlation between phenomena at different scales, compromise between different dominant mechanisms, coupling between spatial and temporal structural changes and critical phenomena occurring in these systems — these are the four critical issues in understanding complex systems. We first propose that by analyzing particle-fluid systems complex systems can be formulated as a multi-objective variational problem. Such an analytical multi-scale method will be reviewed in particular by analyzing the above four critical issues and by showing its 20-year development at IPE from a rough idea to modeling approaches, softwares and finally to industrial applications as well as its extension to different chemical and physical systems. The strategy of “from the particular to the general” in developing this multi-scale methodology is emphasized and challenges to mathematicians and physicists are identified to show the necessity of transdisciplinary cooperation. This presentation will be concluded by prospects and suggestions.     

碰撞振动系统分岔与混沌的研究进展

针对工程实际中普遍存在的碰撞振动系统这种典型的非光滑动力系统, 其研究具有重要的理论意义和工程实用价值. 碰撞振动系统动力学的分析与研究方法主要有理论分析、数值模拟以及应用与实验研究. 为了研究碰撞振动系统的周期运动稳定性、分岔及混沌, 采用的手段有建立Poincar\'{e}映射、中心流形和范式方法, 映射的分岔与混沌理论是碰撞振动系统研究的理论基础. 首先简述了碰撞振动系统的分析与研究方法, 光滑非线性系统动力学的分析方法部分可以推广到碰撞振动系统, 碰撞振动的不连续性导致一些方法的适用性和有效性问题. 进一步综述了碰撞振动系统周期运动稳定性、分岔、混沌及奇异性的理论研究和工程应用现状. 最后着重结合相关离散型映射系统的动力学发展, 对碰撞振动系统的分岔与混沌研究及存在的主要问题进行了讨论, 并展望了其发展趋势.      

On an improved adaptive reduced-order model for the computation of steady-state vibrations in large-scale non-conservative systems with friction joints

Nonlinear Dynamics - Joints are commonly used in many large-scale engineering systems to ease assembly, and ensure structural integrity and effective load transmission. Most joints are designed...     

多级递阶工程系统抗地震设计整体优化的计算实现

针对多级递阶工程系统结构特点 ,以结构设防烈度为优化指标、抗地震设计为工程背景 ,本文建立该系统整体优化的计算方法体系并付诸实现。首先 ,提出大系统整体与局部划分概念 ,从基元系统出发 ,建立有效的离散型最优化方法和算法 ,形成方法体系的基础层次 ;其次 ,根据该系统逻辑分布 ,提出整体优化的耦合法与分解法 ,构成方法体系的上一层次 ;最后 ,通过该系统本体描述数据设计 ,开发了通用分析程序 ,大量运算校验了它们的速度、精度和稳定性     

Nonlinear constitutive force model selection,update and uncertainty quantification for periodically sequential impact applications

Nonlinear Dynamics - Contact–impact events frequently occur between solid contact interfaces in complex dynamic mechanical systems and engineering applications. Impact force models are used...     

Complex dynamics of multi-regional economic interactions

Nonlinear Dynamics - Dynamical systems are being employed over the last decades to investigate complex behaviors in traditional fields as engineering and physics, but also in biology, medicine,...     

Parametric characteristic of the random vibration response of nonlinear systems

Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of nonlinear engineering systems and structures that can be represented by a Volterra series model.In the present study,the random vibration of nonlinear systems is investigated using Volterra series.Analytical expressions were derived for the calculation of the output power spectral density(PSD) and input-output cross-PSD for nonlinear systems subjected to Gaussian excitation.Based on these expressions,it was revealed that both the output PSD and the input-output crossPSD can be expressed as polynomial functions of the nonlinear characteristic parameters or the input intensity.Numerical studies were carried out to verify the theoretical analysis result and to demonstrate the effectiveness of the derived relationship.The results reached in this study are of significance to the analysis and design of the nonlinear engineering systems and structures which can be represented by a Volterra series model.     

Residual Stresses in Cu/Ni Multilayer Thin Films Measured Using the Sin2ψ Method

Experimental Mechanics - Residual stresses in multilayer thin films are of substantial importance to the service life of advanced engineering systems. In this investigation, the residual stresses...     

充液系统动力学与航天高技术问题

充液航天器内部液体晃动及其对控制系统的影响,是当前国内外航天高技术研究的重要课题,也是一个比较复杂的问题。本文首先由力学变分原理导出了充液系统的状态方程,其次分析了充液系统的稳定性;特别是,研究了在失重或微重条件下,充液航天器内部液体晃动的动力学特性以及部分充液三轴稳定性问题等。本文的研究结果,对于航天、航空、航海中的充液系统动力学与控制问题,都有重要的参考价值。      

Transmissibility function-based fault diagnosis methods for beam-like engineering structures: a review of theory and properties

Nonlinear Dynamics - The beam-like structures commonly exist in engineering systems and there are many critical issues relevant to fault diagnosis of those structures. Noticeably, among all other...     

基于降维积分的结构系统可靠性分析研究

复杂结构系统一般具有多个失效模式. 传统系统可靠性分析模型是在假设各失效模式相互独立的条件下建立的. 而在工程实际问题中,由于结构系统的组成单元之间紧密联系,系统的失效模式大多是相互耦合的. 简单地在失效模式相互独立的假设条件下进行系统可靠性分析与评价常常会导致过大的误差,甚至得出错误的结论. 提出一种相关失效模式结构系统可靠性分析方法. 利用降维法和Gauss-Hermite数值积分技术计算随机参数结构系统极限状态函数的统计矩,采用极限状态函数的前四阶累积量拟合其累积量生成函数,通过鞍点逼近方法拟合结构系统极限状态函数的概率密度函数和累积分布函数,进而获取结构系统的可靠度(或失效概率).数值算例表明该方法具有较高的计算精度和效率,通用性强.     

Dynamic response of objects with shock-absorbers to seismic loads

The paper outlines a mathematical model describing the vibrations of buildings and engineering structures with general-type passive shock-absorbers, rigid bodies, and ideal constraints. Two modifications of systems with passive shock absorbers are considered assuming constancy of their structure. These systems are studied numerically; the dynamic processes excited in them are compared __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 127–137, December 2007.