Variational iteration solving method for El Nio phenomenon atmospheric physics of nonlinear model

A class of E1 Niйo atmospheric physics oscillation model is considered. The E1 Niйo atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The conceptual oscillator model should consider the variations of both the eastern and western Pacific anomaly patterns. An E1 Niйo atmospheric physics model is proposed using a method for the variational iteration theory. Using the variational iteration method, the approximate expansions of the solution of corresponding problem are constructed. That is, firstly, introducing a set of functional and accounting their variationals, the Lagrange multiplicators are counted, and then the variational iteration is defined, finally, the approximate solution is obtained. From approximate expansions of the solution, the zonal sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the sea-air oscillation for E1 Niйo atmospheric physics model can be analyzed. E1 Niйo is a very complicated natural phenomenon. Hence basic models need to be reduced for the sea-air oscillator and are solved. The variational iteration is a simple and valid approximate method.

Nonlinear phenomena in dielectric barrier discharges: pattern, striation and chaos

The nonlinear phenomenon is very popular in dielectric barrier discharge （DBD） plasmas. There are at least three kinds of spatial and temporal nonlinear phenomena appearing synchronously or asynchronously in DBDs, i.e. self-organized patterns, striations and chaos. This paper describes the recent research and progress in understanding the nature of these nonlinear phenomena. Patterns are macroscopic structures with certain spatial and/or temporal periodicities generated through self- organization of microscopic parameters. The physics of patterns in DBDs is mainly associated with lateral dynamic behaviors or the lateral non-local effect of charged particles resulting in the lateral development or non-uniformity of discharge. Striations are ionization waves with unique properties determined by transport phenomena, ionization processes and electron kinetics in current-carrying plasmas. The physics of striations in DBDs is mainly associated with the advances in non-local electron kinetics in spatially inhomogeneous plasmas. Chaos is a kind of random and non-periodic phenomenon occunfng in a determined dynamic system, following a series of certain rules while exhibiting random locomotion, and is regarded as an intrinsic and ubiquitous phenomenon in a nonlinear dynamic system. An evolution trajectory including period-doubling bifurcation to chaos was observed in DBDs or DBD-derived plasmas. In a common sense, it is believed that the formation of all the three nonlinear phenomena in a DBD system should be related to the non-local transversal and/or longitudinal dynamics of space charges （i.e. non-local effect） or the localized electric field interaction. Future work is still needed on the underlying physics and should be directed to pursuing the unification of these nonlinear phenomena in DBD.

A workload-based nonlinear approach for predicting available computing resources

Performance degradation or system resource exhaustion can be attributed to inadequate computing resources as a result of software aging.In the real world,the workload of a web server varies with time,which will cause a nonlinear aging phenomenon.The nonlinear property often makes analysis and modelling difficult.Workload is one of the important factors influencing the speed of aging.This paper quantitatively analyzes the workload-aging relation and proposes a framework for aging control under varying workloads.In addition,this paper proposes an approach that employs prior information of workloads to accurately forecast incoming system exhaustion.The workload data are used as a threshold to divide the system resource usage data into multiple sections,while in each section the workload data can be treated as a constant.Each section is described by an individual autoregression(AR)model.Compared with other AR models,the proposed approach can forecast the aging process with a higher accuracy.

Integration of a nonlinear energy sink and a piezoelectric energy harvester

A mechanical-piezoelectric system is explored to reduce vibration and to harvest energy. The system consists of a piezoelectric device and a nonlinear energy sink （NES）, which is a nonlinear oscillator without linear stiffness. The NES-piezoelectric sys- tem is attached to a 2-degree-of-freedom primary system subjected to a shock load. This mechanical-piezoelectric system is investigated based on the concepts of the percentages of energy transition and energy transition measure. The strong target energy transfer occurs for some certain transient excitation amplitude and NES nonlinear stiffness. The plots of wavelet transforms are used to indicate that the nonlinear beats initiate energy transitions between the NES-piezoelectric system and the primary system in the tran- sient vibration, and a 1：1 transient resonance capture occurs between two subsystems. The investigation demonstrates that the integrated NES-piezoelectric mechanism can re- duce vibration and harvest some vibration energy.

A PREDICT-CORRECT NUMERICAL INTEGRATION SCHEME FOR SOLVING NONLINEAR DYNAMIC EQUATIONS

A new numerical integration scheme incorporating a predict-correct algorithm for solving the nonlinear dynamic systems was proposed in this paper. A nonlinear dynamic system governed by the equation v = F（v, t） was transformed into the form as v = Hv ＋ f（v, t）. The nonlinear part f（v, t） was then expanded by Taylor series and only the first-order term retained in the polynomial. Utilizing the theory of linear differential equation and the precise time-integration method, an exact solution for linearizing equation was obtained. In order to find the solution of the original system, a third-order interpolation polynomial of v was used and an equivalent nonlinear ordinary differential equation was regenerated. With a predicted solution as an initial value and an iteration scheme, a corrected result was achieved. Since the error caused by linearization could be eliminated in the correction process, the accuracy of calculation was improved greatly. Three engineering scenarios were used to assess the accuracy and reliability of the proposed method and the results were satisfactory.

Dynamic analysis of two-degree-of-freedom airfoil with freeplay and cubic nonlinearities in supersonic flow

The nonlinear aeroelastic response of a two-degree-of-freedom airfoil with freeplay and cubic nonlinearities in supersonic flows is investigated. The second-order piston theory is used to analyze a double-wedge airfoil. Then, the fold bifurcation and the amplitude jump phenomenon are detected by the averaging method and the multi-variable Floquet theory. The analyticall results are further verified by numerical simulations. Finally, the influence of the freeplay parameters on the aeroelastic response is analyzed in detail.

电压控制型Buck变换器的混沌抑制策略

针对降压(Buck)变换器运行过程中所产生的混沌现象,根据变换器的工作特性确立其数学模型,并分析其通往混沌的道路。分别使用了两种控制策略使系统稳定于周期1状态:第一种是设计非线性控制器,施加该控制器后,系统的动态响应快,抗扰性强,但输出电压与参考值有一定的偏差;第二种是基于终端滑模自抗扰控制(TSMADRC)的双闭环控制策略,使用该控制策略后,系统输出超调量小、动态响应快且具有较好的暂态响应,并且从源头上避免了混沌现象的发生。仿真结果表明,两种控制方法均可以抑制混沌现象的发生,使Buck变换器工作于稳定的周期1状态。

基于迭代学习辨识算法的非线性宏观交通流参数优化

考虑到迭代学习辨识算法具有的独特优势,设计了一种基于迭代学习辨识算法的非线性宏观交通流参数优化方法。通过一个城市道路网络的模拟实验表明,该方法能够有效地识别时变量多参数的动态系统。研究结果表明:采用VISSIM的路段评估函数对各个路段的密度和车速进行采集,可方便对迭代式识别方法评估结果进行比较。随着迭代次数的增多,网络各个路段排队车错误值逐渐降低,且保持不变。对网络交通系统的最大错误对比,更好地体现了迭代识别的正确性。道路网的非线性宏观流量模型与道路模拟实验结果总体上与道路交通流量的实际改变相一致,验证了该方法在道路网络中的非线性大流量模型的识别性能。

基于小增益定理的非线性系统的事件触发控制

利用一个指数小增益定理,对一类非线性控制系统提出一种事件触发控制策略.利用该策略,实现了该系统指数渐近稳定,同时有效避免了Zeno现象的发生,最后数值模拟验证了结论的有效性.

相邻两海域渔业资源模型的动力学分析

在考虑相邻海域相互作用的前提下,引入鱼类自然增长、人类捕捞等因素,建立相邻两海域的渔业资源模型。首先利用雅可比矩阵等相关理论知识分析了Nash均衡点及边界均衡点的稳定性,然后通过数值模拟讨论该模型的分岔行为及多稳态现象,最后利用分岔图、最大Lyapunov指数、吸引子和吸引盆等工具,深入讨论了相关参数对渔业资源存量的影响。研究结果揭示了相邻两海域的渔业资源之间复杂的相互作用关系,表明了当参数处于一定范围时,渔业资源才能保持稳定,才更有利于资源的可持续发展。

电磁加载对超声传播特性的影响

近年来,非线性超声技术在检测结构微损伤方面的能力引起了国内外学者广泛的关注。如何提高闭合裂纹引起的非线性声学响应是非线性超声检测技术要解决的关键问题。本文提出利用电磁加载的方式激励闭合裂纹处于动态扩展状态,并实现对超声的调制过程,进而产生较为强烈的超声非线性效应。通过研究电磁加载过程对闭合裂纹的激励效果,分析不同电磁加载参数对超声传播过程的影响特性,给出超声回波信号与电磁加载之间的对应关系,为超声非线性检测技术的工程应用提供重要依据。

故障诊断中非线性耦合特征提取方法研究

本文在高阶谱域研究故障诊断中非线性耦合特征提取,为了简化计算并得到有效的二次相位耦合特征,将双相干特征的计算转化到极坐标下进行.在分析故障机理的基础上,仅通过计算几个角切片来提取特征,该思想很易于推广到其它高阶方法中.最后,通过对轴承进行实验证明了该方法的有效性.

不平衡磁拉力作用下水轮发电机组转子系统碰摩动力学分析

根据大型旋转机械机电耦联特性,建立了水轮发电机组转子-轴承系统在不平衡磁拉力(UnbalancedMagnetic Pull,UMP)作用下定子与转子碰摩模型及其运动微分方程。利用数值积分方法,对系统由于励磁电流、转子质量偏心以及定子径向刚度变化引起的非线性动力学行为进行了研究,并给出了相应的分岔图、Poincaré映射图、时域图和频谱图。计算结果表明:UMP的存在使系统响应呈现出周期1、周期5、拟周期以及混沌等复杂的动力学现象并对其稳定性造成了明显影响;此外,较大的转子质量偏心以及定子径向刚度均有可能使局部碰摩发展为全周碰摩,对定子和转子造成巨大损害。

电流控制反激式变换器动力学特性研究

利用变压器原副边电流安匝和作为状态变量之一,建立了具有两条安匝和边界的电流控制反激式变换器的离散时间模型,并采用Jacobi矩阵求特征值导出了最大Lyapunov指数。进一步地,利用分岔图和最大Lyapunov指数谱,进行了反激式变换器的分岔分析和工作状态域估计。PSIM电路仿真结果验证了理论分析的正确性,表明了电流控制反激式变换器在参数变化时,存在倍周期分岔、边界碰撞分岔、混沌、周期窗等复杂非线性现象,有着周期态、CCM鲁棒混沌态和DCM弱混沌态三种不同的工作状态。

电液伺服系统非线性振动机理及试验研究

电液伺服系统是非线性动力学系统,在工作过程中容易出现非线性振动、噪声、冲击和爬行等异常现象,而且诱因不易确定,严重影响系统的稳定性。根据非线性动力学原理,建立电液伺服系统的非线性动力学模型。通过理论研究,探索非线性液压弹簧力和非线性摩擦力等非线性因素对系统动力学特性的影响规律。指出非线性液压弹簧力作用可以用Duffing方程描述,非线性摩擦力作用可以用Van Der Pol方程描述。用研究非线性动力学系统的有效方法:时间历程、频闪采样、功率谱等,对实测信号进行深入分析,多方位揭示电液伺服系统非线性振动的机理及诱因。结果表明,非线性液压弹簧力引起的'跳跃现象'和非线性摩擦力引起的极限环型振荡的共同作用是导致系统发生非线性振动的一个主要诱因,值得关注。

涡旋相互作用及其对强度和路径的影响

研究一个台风涡旋和一个低压涡旋之间的相互作用。该相互作用使低压涡旋强度衰减的速率显著变慢， 使低压涡旋滞留在初始位置附近的时间显著加长。在低压涡旋强度演化和路径变化的过程中， 显示出清楚的临界点现象。

S_2O_8^(2-)恒电流还原过程中新的非线性现象研究

报道在1mol／dm3NaOH溶液中于银电极上恒电流还原条件下的电势振荡现象。测定了该振荡反应在电流浓度参数平面上的分合边界图。除了一些出现在上边界处的阻尼振荡以外，还给出了在固定浓度时单调地增加所控电流在边界内产生的典型的电势振荡序列。该振荡现象可用双稳态与正负反馈相偶联来解释，电流扫描和循环伏安实验结果支持这种解释。研究结果表明，除（电）化学反应外，交替为主的扩散和对流物理体质过程在该振荡中起重要作用。

液压缸低速运动的动态分析

通过理论分析和试验验证研究了液压缸运动的非线性动态特征。提出弹簧刚度随活塞位移变化和工作状态不同而呈现出软硬弹簧特性的非线性弹簧力特征,其作用效果可以用有阻尼的Duffing方程来近似描述;摩擦力随速度的变化遵循Streibeck曲线,其作用效果随工作点在曲线上所处区段而异,可以用van der Pol方程来近似描述。指出液压缸低速爬行是在特定工况下的“跳跃现象”、自激振动等多重作用的结果。

行波超声电机定子的非线性振动(英文)

分析了超声电机定、转子间接触力的非线性特性引起的旋转型行波超声电机(TWUM)定子的非线性振动,以此为基础,建立了TWUM定子的非线性振动模型,并用KBM法求解了该模型。求解结果表明,定子的振动是非线性的,且会产生非线性的跳跃和迟滞现象,定子的非线性振动还会使TWUM输出的堵转力矩也出现跳跃现象。基于实验测得的TRUM空载转速的跳跃对定子的非线性振动进行了验证。在此基础上,对影响定、转子间接触力的几个因素进行了分析。分析结果表明,定子上的激励电压越高,施加在定、转子间的预压力越小,定、转子间相对滑动的摩擦系数越小;定子齿越短,摩擦材料越软,定子振动的非线性现象就越不明显,TWUM的运行稳定性就越好,TWUM的工作频带也就越宽。

四阶忆阻考毕兹混沌振荡器研究

通过在三阶考毕兹混沌振荡器中引入一阶广义忆阻器,提出了一种新颖的四阶忆阻考毕兹混沌振荡器,其中一阶广义忆阻器由二极管桥级联一阶RC滤波器构成。建立了忆阻考毕兹混沌振荡器的动力学模型,研究了它的平衡点和稳定性,结果表明:四阶忆阻考毕兹混沌振荡器具有唯一的不稳定鞍焦。进一步开展了依赖于电路元件参数的动力学特性研究。采用理论分析、数值仿真和实验验证相结合的方法,对电路展现出的混沌吸引子、周期极限环等复杂的非线性现象进行了研究,实验结果与数值仿真结果相一致,较好地验证了理论分析结果。