Describing functions for nonlinear optical systems

The concept of describing functions is useful for analyzing and designing nonlinear systems. A proposal for using the idea of describing functions for studying the behavior of a nonlinear optical processing system is given. The describing function can be used in the same way that a coherent transfer function or optical transfer function is used to characterize linear, shift-invariant optical processors. Two coherent optical systems for measuring the magnitude of the describing function of nonlinear optical processors are suggested.     

Evaluation of intratympanic formulations for inner ear delivery: methodology and sustained release formulation testing

A convenient and efficient in vitro diffusion cell method to evaluate formulations for inner ear delivery via the intratympanic route is currently not available. The existing in vitro diffusion cell systems commonly used to evaluate drug formulations do not resemble the physical dimensions of the middle ear and round window membrane. The objectives of this study were to examine a modified in vitro diffusion cell system of a small diffusion area for studying sustained release formulations in inner ear drug delivery and to identify a formulation for sustained drug delivery to the inner ear. Four formulations and a control were examined in this study using cidofovir as the model drug. Drug release from the formulations in the modified diffusion cell system was slower than that in the conventional diffusion cell system due to the decrease in the diffusion surface area of the modified diffusion cell system. The modified diffusion cell system was able to show different drug release behaviors among the formulations and allowed formulation evaluation better than the conventional diffusion cell system. Among the formulations investigated, poly(lactic-co-glycolic acid)–poly(ethylene glycol)–poly(lactic-co-glycolic acid) triblock copolymer systems provided the longest sustained drug delivery, probably due to their rigid gel structures and/or polymer-to-cidofovir interactions.     

A second-order reduced multiscale method for nonlinear shell structures with orthogonal periodic configurations

This article develops an efficient second-order reduced multiscale (SORM) method to study the nonlinear shell structure with orthogonal periodic configurations. The heterogenous shell structure is periodically distributed in orthogonal curvilinear coordinate systems. At first, the nonlinear problems for the shell structure are introduced, and the detailed higher-order nonlinear multiscale formulas based on the asymptotic homogenization approach are given including microscale unit cell functions, effective material parameter and the homogenized equation. Also, since it requires a large number of computation cost to solve the nonlinear multiscale problems by the traditional high-order homogenization methods, the novel reduced order multiscale model is constructed. Further, according to the reduced-order multiscale models and higher-order nonlinear formulas, an effective SORM algorithm is provided for studying the nonlinear shell structures. The main characteristics of the proposed algorithm are that the novel reduced forms established to investigate the nonlinear shell structures and an efficient higher-order homogenized solution evaluated by postprocessing that does not need higher-order continuities of the homogenization solutions. Finally, according to some typical nonlinear examples including block structures, cylindrical shell and double-curved shallow shell, the availabilities of the SORM algorithm are confirmed.     

Control of chaos in nonlinear systems with time-periodic coefficients

In this study, some techniques for the control of chaotic nonlinear systems with periodic coefficients are presented. First, chaos is eliminated from a given range of the system parameters by driving the system to a desired periodic orbit or to a fixed point using a full-state feedback. One has to deal with the same mathematical problem in the event when an autonomous system exhibiting chaos is desired to be driven to a periodic orbit. This is achieved by employing either a linear or a nonlinear control technique. In the linear method, a linear full-state feedback controller is designed by symbolic computation. The nonlinear technique is based on the idea of feedback linearization. A set of coordinate transformation is introduced, which leads to an equivalent linear system that can be controlled by known methods. Our second idea is to delay the onset of chaos beyond a given parameter range by a purely nonlinear control strategy that employs local bifurcation analysis of time-periodic systems. In this method, nonlinear properties of post-bifurcation dynamics, such as stability or rate of growth of a limit set, are modified by a nonlinear state feedback control. The control strategies are illustrated through examples. All methods are general in the sense that they can be applied to systems with no restrictions on the size of the periodic terms.     

Applications of a reduction method for reanalysis to nonlinear dynamic analysis of framed structures

 This paper is concerned with the nonlinear dynamic analysis of framed structures using a reduction method recently proposed by the authors. The reduction method is originally devised for structural static reanalysis and has been applied in optimal design of structures to speed up the design process. For nonlinear dynamic analysis of framed structures, the incremental or iterative equations of motion can be transformed into an algebraic system of equations if appropriate integration methods such as Newmark's method are used to integrate the equations of motion. The resulting algebraic system, referred to as the effective system in this paper, changes during the simulation for a nonlinear dynamic problem. Therefore, from the point of view of solving systems of equations, a nonlinear dynamic problem is very similar to an optimal design problem in that the system of equations changes for both types of problems. Hence, any reanalysis technique can be readily applied to carry out a nonlinear dynamic analysis of structures. As demonstrated from the presented numerical examples, the response obtained by the adopted reduction method is as accurate as that obtained by the Cholesky method, and as estimated from the operation counts involved in the method, it is more efficient than the Cholesky method when the half-band width is greater than about 50. Received 23 March 2000     

多自由度裂纹转子系统非线性动力学特性分析

大型旋转机械转轴裂纹具有复杂的高维非线性特征, 由此产生的机械故障时有发生。本文根据某航空发动机低压转子系统,利用拉格朗日原理建立了具有26个自由度的含有裂纹故障的高维非线性动力学模型。引进改进的POD方法成功将该系统降为具有两个自由度含有特征的低维非线性系统。数值模拟结果显示降维系统具有与原系统一致的非线性动力学特征,表明本方法对解决高维非线性问题具有较好的有效性。此外,本文还利用C-L方法对其进行分岔分析,讨论了系统参数与系统动态行为之间的关系,得到了裂纹转子各种不同分岔模式,得到了裂纹二分之一亚谐共振条件下的非线性动力学特性, 准确反映了裂纹转子的动力学特征。     

主余震序列作用下非线性单自由度体系的增量损伤分析

同时采用真实主余震序列和人工构造主余震序列作为输入,开展了非线性单自由度体系在主余震序列作用下的增量损伤分析。挑选75组真实主余震序列,并基于相同的主震记录,分别采用重复法、随机法和衰减法构造不同的人工主余震序列作为输入。分别采用理想弹塑性模型、考虑屈服后刚度的双线型模型和三线型模型,开展主余震序列作用下非线性单自由度体系的反应分析。以修正的Park-Ang损伤指数作为结构损伤指标,对主余震序列作用下的结构增量损伤进行研究,并对强度折减系数、恢复力模型及主余震序列人工构造方法对增量损伤的影响进行研究。结果表明：余震造成的结构增量损伤不可忽视。基于重复法和随机法合成的人工主余震序列相比真实主余震序列的余震强度偏大,因此会高估余震对结构造成的增量损伤。基于衰减法合成的人工主余震序列的余震强度偏小,会低估余震对结构造成的增量损伤。结构特性对增量损伤的影响很小,体现为不同强度折减系数及不同恢复力模型对结构增量损伤的影响均不明显。     

非线性被动动力减振器对高耸结构风振控制的实用设计方法

以两个被控结构风振反应的控制效果相等为原则，本文建立了非线性被动动力减振器对高耸结构脉动风振反应控制的等效TMD方法。文中利用求出的等效TMD动力参数和TMD对结构风振反应控制效果等效结构阻尼比的概念，提出了基于中国荷载规范的非线性被动动力减振器对高耸结构风振控制的设计方法。     

Application of the proper orthogonal decomposition for linear and nonlinear structures under transient excitations

Model reduction has become very important in order to save calculation time. In particular, in structural dynamics, computations become very time-consuming when the critical time step of explicit integrators becomes very small. The main focus of this paper is on the application of the Proper Orthogonal Decomposition (POD) method to a structure subjected to transient earthquake loading. It is shown that based on the information of only a small portion of the transient excitation and the structure (“snapshots”), it is possible to assemble a reduced-order model, which yields a very accurate and time-saving approximation of the response to the entire earthquake. The POD reduction method is applied not only to linear, but also to nonlinear structures under earthquake loading. In the linear case, the POD results can be compared to those obtained by the classical method of modal truncation. In the nonlinear case, base isolation systems (friction pendulum systems) are integrated in the structure. Error estimations are applied in order to assess the solution of the POD-reduced system of the linear and the nonlinear systems. The POD can be applied successfully if the snapshots within the chosen time interval describe the main behavior of the system well. In both the linear and nonlinear cases, the approximation of the system as reduced by the POD is very accurate even if only a few POD modes are used. The advantage over the method of Modal Truncation is not only the optimality of the POD modes concerning their associated energy, but also its applicability to nonlinear systems.     

6061铝合金分别在Q235钢和纯钛表面的反应润湿

采用座滴法在高真空条件下研究了熔融6061铝合金在600~700℃分别与Q235钢和纯钛的润湿行为。研究表明两者都为典型的反应润湿,且最终润湿性随着温度的升高而改善;界面反应的自由能变化对最终润湿性及界面结构影响较小,而基板金属在铝中的溶解度不同决定了界面反应层厚度(即溶解度越大则反应层越厚);三相线附近的还原反应诱发了前驱膜的产生,且最终润湿性越好则前驱膜越宽;两者体系的铺展动力学均可以由RPC模型描述:在Al/Ti体系中整个润湿过程分为两个阶段,即先非线性铺展,后线性铺展阶段,两个阶段的铺展活化能分别为72kJ/mol、118kJ/mol,且界面上存在Si的富集;在Al/Q235钢体系中整个润湿过程呈线性铺展,铺展活化能为86kJ/mol,无Si元素在界面富集。     

Time-correlated single photon counting system and light-collection system for studying fluorescence emitters under high-vacuum conditions: Use of immersion objective and ionic liquid

In this paper, we introduce a time-correlated single photon counting system and an efficient light-collection system for studying fluorescence emitters under high-vacuum conditions; the latter system has an immersion objective, and an ionic liquid is used as a refractive index matching medium. The ionic liquid is positioned in high vacuum. The time-correlated single photon counting system has modified photomultiplier tubes that act as photon detectors. The light-collection system is designed to be simple, compact, and easy to use. In order to verify the performance of these systems, the optical properties of colloidal semiconductor nanocrystals (CdSe/ZnS) and fluorescent dye molecules are studied as examples.     

Data based model free hysteresis identification for a nonlinear structure

In the last two decades, the damage detection for civil engineering structures has been widely treated as a modal analysis problem and most of the currently available vibration-based system identification approaches are based on modal parameters, namely the natural frequencies, mode shapes and damping ratios, and/or their derivations, which are suitable for linear systems. Nonlinearity is generic in engineering structures. For example, the initiation and development of cracks in civil engineering structures as typical structural damages are nonlinear process. One of the major challenges in damage detection, early warning and damage prognosis is to obtain reasonably accurate identification of nonlinear performance such as hysteresis which is the direct indicator of damage initiation and development under dynamic excitations. In this study, a general data-based identification approach for hysteretic performance in form of nonlinear restoring force using structural dynamic responses and complete and incomplete excitation measurement time series was proposed and validated with a 4-story frame structure equipped with smart devices of magneto-rheological (MR) damper to simulate nonlinear performance. Firstly, as an optimization method, the least-squares technique was employed to identify the system matrices of an equivalent linear system of the nonlinear structure model basing on the excitation force and the corresponding vibration measurements with impact test when complete and incomplete excitations; and secondly, the nonlinear restoring force of the structure was identified and compared with the test measurements finally. Results show that the proposed data-based approach is capable of identifying the nonlinear behavior of engineering structures and can be employed to evaluate the damage initiation and development of different structure under dynamic loads.     

Nonlinear dynamic state estimation in instrumented structures with conditionally linear Gaussian substructures

Many problems of state estimation in structural dynamics permit a partitioning of system states into nonlinear and conditionally linear substructures. This enables a part of the problem to be solved exactly, using the Kalman filter, and the remainder using Monte Carlo simulations. The present study develops an algorithm that combines sequential importance sampling based particle filtering with Kalman filtering to a fairly general form of process equations and demonstrates the application of a substructuring scheme to problems of hidden state estimation in structures with local nonlinearities, response sensitivity model updating in nonlinear systems, and characterization of residual displacements in instrumented inelastic structures. The paper also theoretically demonstrates that the sampling variance associated with the substructuring scheme used does not exceed the sampling variance corresponding to the Monte Carlo filtering without substructuring.     

基于压电元件的半主动振动控制的研究

为了克服主/被动控制中存在的缺点,提出了一种基于同步开关阻尼技术的半主动振动控制新方法.基于该方法的控制系统简单,只要一些电子元器件就可以实现振动控制,且控制效果好、鲁棒性高.采用此方法能有效对悬臂复合梁进行了振动控制.由于半主动控制方法的控制效果主要取决于电路品质因子以及开关切换的延时时间,因此通过探讨这两个参数对控制效果的影响,推导了基于开关切换延时的半主动振动控制的阻尼公式,搭建了悬臂复合梁振动半主动实验平台,对理论分析结果进行了实验验证.     

拉索_网壳结构的动力特性和非线性动力反应

将空间网壳结构与拉索有机结合便形成拉索-网壳结构体系。该体系不但具有美学特征，更可进一步增大跨度。基于泰勒数学展开公式和变分原理，推导了具有二阶精度的空间杆单元几何非线性刚度矩阵；研究了拉索单元非线性问题，得出了其切线刚度矩阵；给出了结构非线性力学响应计算策略等。通过数值计算，分析了结构动力特性和非线性地震动力响应问题。计算结果显示，拉索-网壳结构的自振频率皆明显高于对应的网壳结构，且频谱较为密集，甚至不同序号的自振频率几乎相同，拉索-网壳结构的地震动力响应不但与拉索长度、截面尺寸、预拉力和布置方式有关，还与塔柱高度、截面尺寸等有关。     

基于系统输出频率响应函数的非线性系统研究

根据非线性系统输出频率响应函数(output frequency response functions,OFRF)理论,研究了系统输出频谱与参数之间的关系,提出一种研究非线性系统特性的新方法.该方法可以通过一个多项式清晰地表达出非线性系统输出频谱与非线性项参数之间关系,为非线性系统设计、研究及故障诊断打下一个重要的基础...     

The role of material nonlinearities in composite structures

In today's global market the optimal use of composites, to fulfil their potential for weight savings, is now being increasingly pursued as a means of obtaining a competitive advantage. However, the optimum design of composite structures and bonded composite joints requires a detailed understanding of the fundamental mechanical behaviour of composite materials and the adhesive systems. Whereas the time-dependent behaviour of the adhesive systems is reasonably well documented and has, to some degree, been accounted for in the design of bonded joints this has not yet occurred for advanced graphite-epoxy composites. Indeed, although it is recognised that the matrix-dominated response of many composite materials and structures is highly nonlinear, even at room temperature, this is often neglected in the design process. This restriction means that the full potential of the fibre matrix system may not be achieved. To this end the present paper, which focuses on the (matrix dominated) shear stress-shear strain behaviour of the AS4/3501-6 graphite-epoxy resin system, presents the results of an experimental investigation into the nonlinear behaviour of graphite-epoxy.     

结构随机延性需求谱的应用研究

结构的地震反应危险性曲线体现了结构的地震反应与地震动强度之间的关系,采用随机延性需求谱可以很方便地建立结构的地震反应危险性曲线。非线性结构在随机地震作用下的位移反应分析属于非线性随机振动问题,采用随机延性需求谱可以简单而有效的获得非弹性单自由度体系的随机位移反应的统计量,结合非线性静力分析,还可以进行多自由度结构的随机地震反应分析。此外,随机延性需求谱还可以用于结构的抗震可靠度分析。