非惯性参考系中弹性壳的非线性振动分析

给出了弹性壳处于非惯性参系中的运动描述，基于Ｈａｍｉｌｔｏｎ原理建立了中厚壳在非惯性参考系中的非线性运动控制方程，应用多尺度法及谐波平衡法具体地分析了圆柱壳的非线性振动问题     

圆柱壳的非线性自由振动分析

本文分析了各向同性封闭圆柱壳的非线性自由振动。文中采用经典的非线性弹性力学方法推导了圆柱壳的大振幅运动方程,这些方程的静态形式与冯·卡门的板理论方程具有同样的精度。文中讨论了四种基本振动模态,并且还以数学公式的形式给出了一般的最终结果,一些例子以曲线给出结果,并进行了比较。结果还表明线性振动可以作为非线性振动的一种特例。     

一般叠层圆柱厚壳的非线性动力稳定性分析

基于Ｔｉｍｏｓｈｅｎｋｏ－Ｍｉｎｄｌｉｎ假设及Ｈａｍｉｌｔｏｎ原理，建立了一般纤维叠层圆柱厚壳在参数激励下的非线性振动方程；应用多模态近似和增量谐波平衡法求解了叠层圆柱厚壳的非线性动力稳定性问题。横向剪切变形、端部支承条件等因素的影响被讨论。     

一般叠层圆柱厚壳的非线性动力稳定性分析

基于Ｔｉｍｏｓｈｅｎｋｏ－Ｍｉｎｄｌｉｎ假设及Ｈａｍｉｌｔｏｎ原理，建立了一般纤维叠层圆柱厚壳在参数激励下的非线性振动方程；应用多模态近似和增量谐波平衡法求解了叠层圆柱厚壳的非线性动力稳定性问题。横向剪切变形、端部支承条件等因素的影响被讨论。     

钢筋混凝土壳体的非线性分析

本文采用有限元数值方法，分析计算了大型钢筋混凝土壳的几何、物理非线性静力问题，对非线性方程组的求解，文中提出了一种将载荷增量和位移增量相结合的合理方法，保证了在临界点附近迭代法的收敛性，最后，文中通过对实际双曲冷却塔壳的分析，得到了一些对实际工程设计具有指导意义的有益结论。     

带初始几何缺陷FGM固支圆柱壳的非线性动力学分析

本文主要研究了带初始几何缺陷的功能梯度固支圆柱壳在不同体积分数下的非线性动力学行为。假定该功能梯度圆柱壳材料的组分是沿厚度的方向呈梯度几何变化的。运用经典板壳理论、von-Karman几何非线性应变位移关系以及Hamilton原理,推导出两端固支FGM圆柱壳的偏微分非线性运动控制方程。本文考虑了圆柱壳的对称模态,利用Galerkin法对上述非线性动力学方程进行截断,得到常微分形式的非线性动力学方程。主要运用Runge-Kutta法进行数值仿真,并且画出了其最大lyapunov指数图,主要研究了面内载荷对振动响应的影响,并对比了不同体积分数对系统非线性动力学的影响。     

钢筋混凝土板壳材料非线性分析的有限条法

本文发展了变厚度任意配筋的钢筋混凝土板壳问题中考虑材料非线性分析的有有限条法。文中建立了沿厚度方向作分层离散的维蜕化二次厚壳条，而在计算上，沿壳条跨度方向采用Ｓｉｍｐｓｏｎ积分技术可以方向地处理该方向的任意配筋并给出了满足精度要求的选取Ｓｉｍｐｓｏｎ积分点数的表达式。文中提出的“拟刚度矩阵”法大大简化了非线性有限条法的求解过程，给出两个数值算例表明了理论方法的有效性及其精度。     

带频率约束的浸水圆柱壳结构优化设计

与干结构相比，流固耦合系统属于非经典问题，其动态设计要复杂得多。本文基于流固耦合分析，主要探讨了浸水圆柱壳在频率，重量等约束条件下的优化设计问题。针对圆柱壳的结构特点，对壳体，流场分别采用有限条，边界元法进行分析以减小计算量。充分利用系统的灵敏数度信息，采用多目标优化方法对浸水圆柱壳进行了优化设计。通过具体算例证明了本文方法的可行性。     

圆柱壳的非线性动力屈曲分析

本文研究在轴向冲击作用下，具有初始几何缺陷的圆柱壳的非线性弹性动力屈曲问题。由于冲击过程中作用时间极短，应力波的影响变得相当重要，同时认为圆柱壳经历大挠度变形。分析中不仅考虑圆柱壳的径向惯性力，而且也考虑轴向惯性力和几何非线性的影响。假设圆柱壳中位移和薄膜力可分成轴对称分量和非轴对称分量之和，并引入应力函数表示非轴对称内力，对平衡方程应用伽辽金方法，将导出的和冲击物体的质量对动屈曲性能的影响很大。     

可渗透圆柱壳流固耦合问题的流场与内力分析

在弹性薄壳的非线性理论和流体力学基本方程的基础上,研究了可渗透圆柱壳的流固耦合问题.假定壳体具有均布孔隙且孔的面积很小,不考虑其阻力,忽略对弯曲刚度和壳体腔内流体微小运动影响,应用相容欧拉--拉格朗日法建立了带孔的圆柱壳在流体中相互作用的基本方程.通过具体算例求解,给出了流场速度与压力的变化、圆柱壳的变形及内力分布,并对相关参数进行了讨论.     

The X-structure/mechanism approach to beneficial nonlinear design in engineering

Nonlinearity can take an important and critical role in engineering systems, and thus cannot be simply ignored in structural design, dynamic response analysis, and parameter selection. A key issue is how to analyze and design potential nonlinearities introduced to or inherent in a system under study. This is a must-do task in many practical applications involving vibration control, energy harvesting, sensor systems, robotic technology, etc. This paper presents an up-to-date review on a cutting-edge method for nonlinearity manipulation and employment developed in recent several years, named as the X-structure/mechanism approach. The method is inspired from animal leg/limb skeletons, and can provide passive low-cost high-efficiency adjustable and beneficial nonlinear stiffness (high static & ultra-low dynamic), nonlinear damping (dependent on resonant frequency and/or relative vibration displacement), and nonlinear inertia (low static & high dynamic) individually or simultaneously. The X-structure/mechanism is a generic and basic structure/mechanism, representing a class of structures/mechanisms which can achieve beneficial geometric nonlinearity during structural deflection or mechanism motion, can be flexibly realized through commonly-used mechanical components, and have many different forms (with a basic unit taking a shape like X/K/Z/S/V, quadrilateral, diamond, polygon, etc.). Importantly, all variant structures/mechanisms may share similar geometric nonlinearities and thus exhibit similar nonlinear stiffness/damping properties in vibration. Moreover, they are generally flexible in design and easy to implement. This paper systematically reviews the research background, motivation, essential bio-inspired ideas, advantages of this novel method, the beneficial nonlinear properties in stiffness, damping, and inertia, and the potential applications, and ends with some remarks and conclusions.

     

Nonlinear normal modes and their superposition in a two degrees of freedom asymmetric system with cubic nonlinearities

This paper investigates nonlinear normal modes and their superposition in a two degrees of freedom asymmetric system with cubic nonlinearities for all nonsingular conditions, based on the invariant subspace in nonlinear normal modes for the nonlinear equations of motion. The focus of attention is to consider relation between the validity of superposition and the static bifurcation of modal dynamics. The numerical results show that the validity has something to do not only with its local restriction, but also with the static bifurcation of modal dynamics. Project Supported by the National Natural Science Foundation and PSF of China     

Nonlinear time transformation method for strong nonlinear oscillation systems

In this paper, a nonlinear time transformation method is presented for the analysis of strong nonlinear oscillation systems. This method can be used to study the limit cycle behavior of the autonomous systems and to analyze the forced vibration of a strong nonlinear system. The project partly supported by the Foundation of Zhongshan University Advanced Research Center     

An Existence Theorem for Generalized von Kármán Equations

Using techniques from formal asymptotic analysis, the first two authors have recently identified generalized von Kármán equations, which constitute a two-dimensional model for a nonlinearly elastic plate where only a portion of the lateral face is subjected to boundary conditions of von Kármán's type, the remaining portion being free. In this paper, we establish an existence theorem for these equations. To this end, we first reduce them to a single equation, which generalizes a cubic operator equation introduced by M.S. Berger and P. Fife. We then directly solve this equation, notably by adapting a crucial compactness method due to J.-L. Lions. Résumé. En utilisant les techniques de l'analyse asymptotique formelle, les deux premiers auteurs ont récemment identifié des équations de von Kármán généralisées, qui constituent un modèle bi-dimensionnel de plaque non linéairement élastique dont une partie seulement de la face latérale est soumise à des conditions aux limites de von Kármán, la partie restante étant libre. Dans cet article, on établit un théorème d'existence pour ces équations. À cette fin, elles sont d'abord réduites à une seule équation, qui généralise une équation faisant intervenir un opérateur cubique, introduite par M.S. Berger et P. Fife. On résout ensuite directement cette équation, en adaptant notamment une méthode cruciale de compacité due à J.-L. Lions.     

Bifurcations of Nonlinear Normal Modes of Linear Oscillator with Strongly Nonlinear Damped Attachment

Linear oscillator coupled to damped strongly nonlinear attachment with small mass is considered as a model design for nonlinear energy sink (NES). Damped nonlinear normal modes of the system are considered for the case of 1:1 resonance by combining the invariant manifold approach and multiple scales expansion. Special asymptotical structure of the model allows a clear distinction between three time scales. These time scales correspond to fast vibrations, evolution of the system toward the nonlinear normal mode and time evolution of the invariant manifold, respectively. Time evolution of the invariant manifold may be accompanied by bifurcations, depending on the exact potential of the nonlinear spring and value of the damping coefficient. Passage of the invariant manifold through bifurcations may bring about destruction of the resonance regime and essential gain in the energy dissipation rate.     

Distinguishing Periodic and Chaotic Time Series Obtained from an Experimental Nonlinear Pendulum

The experimental analysis of nonlinear dynamical systems furnishes ascalar sequence of measurements, which may be analyzed using state spacereconstruction and other techniques related to nonlinear analysis. Thenoise contamination is unavoidable in cases of data acquisition and,therefore, it is important to recognize techniques that can be employedfor a correct identification of chaos. The present contributiondiscusses the experimental analysis of a nonlinear pendulum, consideringstate space reconstruction, frequency domain analysis and thedetermination of dynamical invariants, Lyapunov exponents and attractordimension. A procedure to construct Poincaré map of the signal ispresented. The analyses of periodic and chaotic motions are carried outin order to establish a difference between them. Results show that it ispossible to distinguish periodic and chaotic time series obtained froman experimental set up employing proper procedures even though noisesuppression is not contemplated.     

Normal Vibrations in Near-Conservative Self-Excited and Viscoelastic Nonlinear Systems

A perturbation methodology and power series are utilizedto the analysis of nonlinear normal vibration modes in broadclasses of finite-dimensional self-excited nonlinear systems closeto conservative systems taking into account similar nonlinear normal modes.The analytical construction is presented for some concretesystems. Namely, two linearly connected Van der Pol oscillatorswith nonlinear elastic characteristics and a simplesttwo-degrees-of-freedom nonlinear model of plate vibrations in agas flow are considered.Periodical quasinormal solutions of integro-differentialequations corresponding to viscoelastic mechanical systems areconstructed using a convergent iteration process. One assumesthat conservative systems appropriate for the dominant elasticinteractions admit similar nonlinear normal modes.     

同伦分析方法：一种不依赖于小参数的非线性分析方法

本文进一步一般化了作者所提出的一种新的非线性分析方法，称为“同伦分析方法”。“同伦分析方法”的最大优点，在于其不依赖小参数，从而可求解更多的非线性问题，甚至包括那些不含小参数的问题。本文给出了几个应用实例，以说明“同伦分析方法”的有效性及巨大的潜力。     

Contrast Enhancement with a Nonlinear Oscillators Network

In this paper, we propose a contrast enhancement realized with a lattice of uncoupled nonlinear oscillators. We show theoretically and numerically that the contrast of a gray scale image is strongly enhanced even if it is initially very weak. An image inversion can also be obtained in real time without needing a reconfiguration of this Cellular Nonlinear Network (CNN). Finally, an electronic implementation of this (CNN) is discussed.     

Singular perturbation of general boundary value problem for nonlinear differential equation system

I.IntroductionAllphysicalsystemsarenonlineartosomeextent.Actually,Lineal.systemisimaginarymodelwherenonlinearfactorisomittedinnonlinearsystem.Insolvingtheautocontl'ol,nonlinearoscillationtheory,theboundarystagnationproblenloffluidIncchanicsandsollleproblemsofsemi-conducttheoryandquantummechanicsetc'.weOnlyncedtosolvethefollowingproblem,whichisnonlineardifferentialequationsystemwithtilesll,allparanletel'inhighestorderderivativeandnonlinearboundaryconditions.whereE>0isasmallparameter,teR,x,fi…