Exact solutions of the nonlinear differential-difference equations associated with the nonlinear electrical transmission line through a variable-coefficient discrete(G'/G)-expansion method

We investigated exact traveling soliton solutions for the nonlinear electrical transmission line. By applying a concise and straightforward method, the variable-coefficient discrete（G /G）-expansion method, we solve the nonlinear differential–difference equations associated with the network. We obtain some exact traveling wave solutions which include hyperbolic function solution, trigonometric function solution, rational solutions with arbitrary function, bright as well as dark solutions.

Disorder Effect on the Transmission of Second Harmonic Waves in One-Dimensional Periodically Poled LiTaO₃

One of the methods for calculating electromagnetic wave dispersion in multi-layer structures is the transfer matrix method. In this paper, we use the transfer matrix method for second harmonic generation in a nonlinear multilayer structure. The nonlinear photonic crystals investigated in this paper are as one-dimensional multi-layered structures including ferroelectric materials such as LiTaO3. Our goal is to investigate the effect of the disorder on the transmission spectrum of electromagnetic waves. Our results showed that positional disorder has different effects on the transmitting band and the gap band. The disorder in the transmitting band reduces the transmission coefficient of the waves and increases the transmission coefficient of the waves in the gap band. Such work has not yet been done on nonlinear photonic crystals producing the second harmonic.

Optimal Design of Aperture Illuminations for Microwave Power Transmission with Annular Collection Areas

This work presents an optimal design method of antenna aperture illumination for microwave power transmission with an annular collection area.The objective is to maximize the ratio of the power radiated on the annular collection area to the total transmitted power.By formulating the aperture amplitude distribution through a summation of a special set of series,the optimal design problem can be reduced to finding the maximum ratio of two real quadratic forms.Based on the theory of matrices,the solution to the formulated optimization problem is to determine the largest characteristic value and its associated characteristic vector.To meet security requirements,the peak radiation levels outside the receiving area are considered to be extra constraints.A hybrid grey wolf optimizer and Nelder–Mead simplex method is developed to deal with this constrained optimization problem.In order to demonstrate the effectiveness of the proposed method,numerical experiments on continuous apertures are conducted;then,discrete arrays of isotropic elements are employed to validate the correctness of the optimized results.Finally,patch arrays are adopted to further verify the validity of the proposed method.

Exact Solutions for a Local Fractional DDE Associated with a Nonlinear Transmission Line

Of recent increasing interest in the area of fractional calculus and nonlinear dynamics are fractional differential-difference equations. This study is devoted to a local fractional differential-difference equation which is related to a nonlinear electrical transmission line. Explicit traveling wave solutions(kink/antikink solitons, singular,periodic, rational) are obtained via the discrete tanh method coupled with the fractional complex transform.

Soliton fusion and fission for the high-order coupled nonlinear Schr?dinger system in fiber lasers

With the rapid development of communication technology,optical fiber communication has become a key research area in communications.When there are two signals in the optical fiber,the transmission of them can be abstracted as a high-order coupled nonlinear Schr¨odinger system.In this paper,by using the Hirota’s method,we construct the bilinear forms,and study the analytical solution of three solitons in the case of focusing interactions.In addition,by adjusting different wave numbers for phase control,we further discuss the influence of wave numbers on soliton transmissions.It is verified that wave numbers k_(11),k_(21),k_(31),k_(22),and k_(32)can control the fusion and fission of solitons.The results are beneficial to the study of all-optical switches and fiber lasers in nonlinear optics.

Closed form soliton solutions of three nonlinear fractional models through proposed improved Kudryashov method

We introduce a new integral scheme namely improved Kudryashov method for solving any nonlinear fractional differential model.Specifically,we apply the approach to the nonlinear space-time fractional model leading the wave to spread in electrical transmission lines(s-tfETL),the time fractional complex Schrödinger(tfcS),and the space-time M-fractional Schrödinger-Hirota(s-tM-fSH)models to verify the effectiveness of the proposed approach.The implementing of the introduced new technique based on the models provides us with periodic envelope,exponentially changeable soliton envelope,rational rogue wave,periodic rogue wave,combo periodic-soliton,and combo rational-soliton solutions,which are much interesting phenomena in nonlinear sciences.Thus the results disclose that the proposed technique is very effective and straight-forward,and such solutions of the models are much more fruitful than those from the generalized Kudryashov and the modified Kudryashov methods.

Fractional soliton dynamics of electrical microtubule transmission line model with local M-derivative

In this paper,two integrating strategies namely exp[-Ф(Х)]and (G'/G^(2))-expansion methods together with the attributes of local-M derivatives have been acknowledged on the electrical microtubule(MT)model to retrieve soliton solutions.The said model performs a significant role in illustrating the waves propagation in nonlinear systems.MTs are also highly productive in signaling,cell motility,and intracellular transport.The proposed algorithms yielded solutions of bright,dark,singular,and combo fractional soliton type.The significance of the fractional parameters of the fetched results is explained and presented vividly.

Nonlinear identification and characterization of structural joints based on vibration transmissibility

In order to investigate the nonlinear characteristics of structural joint,the experimental setup with a jointed mass system is established for dynamic characterization analysis and vibration prediction,and a corresponding nonlinearity identification method is studied.First,the sine-sweep vibration test with different baseexcitation levels areapplied to the structural joint system to study the dominant modal of mass rigid motion.Then,based on t e harmonic balance method principle,t e measured vibration transmissibilities a e utilized for nonlinearity identification using different excitation levels.Experimental results show that nonlinear spring and damping force can be represented by a polynomial order approximation.The identified nonlinear stiffness and damping force can predict the system’s response,and they can reveal t e shifts of resonant frequency or damping due to discontinuity of contact mechanisms within a certain range.

融合历史记忆的单纯形引导鲸鱼优化算法

针对鲸鱼优化算法存在易陷入局部最优、收敛速度慢等缺点,提出一种融合历史记忆的单纯形引导鲸鱼优化算法。首先,为了避免初始化种群过于集中而陷入局部最优,提出了使用混沌映射对初始化种群进行改进,增加了种群多样性;其次,为了解决算法收敛精度低和收敛速度慢的问题,提出了融合历史记忆的单纯形引导策略,利用单纯形法和构建的历史记忆表求解出一个虚拟最优解作为下次随机搜索阶段的引导者,帮助种群在前期的勘探过程中进行细致地搜索;最后提出一种新的非线性参数策略,平衡算法的开发和勘探能力。将算法应用于12个典型的复杂函数优化问题,并与其他5种智能算法比较,实验结果表明,改进后的算法在收敛精度与速度方面均为第一,具有良好的全局搜索能力和局部开发能力。

某金属带式无级变速器振动仿真分析与多工况下试验验证

为分析某金属带式无级变速器(CVT)振动产生机理,采用集中参数法建立双级行星齿轮非线性扭转动力学模型,应用四阶龙格库塔方法进行动态响应求解,利用ADAMS软件进行动力学仿真,对动态响应进行验证,进行CVT振动台架试验测试。研究结果表明:四阶龙格库塔方法与ADAMS动态仿真得到的动态响应结果基本一致;台架试验结果表明前进挡转速为2500 r/min时,低速挡输入轴轴向位置的振动加速度最大为0.623 m/s^(2),转速为1000 r/min时,低速挡输入轴轴向位置的加速度最大为0.309 m/s^(2);倒挡工况下,转速为2500 r/min时,倒挡输入轴轴向位置的振动加速度最大为0.703 m/s^(2),转速1000 r/min时,倒挡输入轴轴向位置的加速度最大为0.504 m/s^(2);倒挡工况下的振动加速度幅值比前进挡高12.85%;倒挡阶次谱中54.4阶和108.8阶振动信号最为明显,挡位切换过程中双级行星齿轮啮合次数增多,啮合间隙是CVT在倒挡动力传递中振动增大的主要原因。

The double auxiliary equations method and its application to space-time fractional nonlinear equations

This paper reflects the execution of a reliable technique which we proposed as a new method called the double auxiliary equations method for constructing new traveling wave solutions of nonlinear fractional differential equation.The proposed scheme has been successfully applied on two very important evolution equations,the space-time fractional differential equation governing wave propagation in low-pass electrical transmission lines equation and the time fractional Burger’s equation.The obtained results show that the proposed method is more powerful,promising and convenient for solving nonlinear fractional differential equations(NFPDEs).To our knowledge,the solutions obtained by the proposed method have not been reported in former literature.

非线性传输线产生射频脉冲原理研究

介绍了非线性传输线的工作原理和色散特性,给出了用于模拟交叉耦合磁饱和非线性传输线的计算方法。算法基于传输线各节点的时域差分方程组进行步进迭代,其中利用J-A模型描述传输线中NiZn铁氧体磁芯的非线性磁化行为,并模拟了非线性传输线的工作方式。实验获得了中心频率165MHz的宽带脉冲输出,初步验证了用于产生宽带电磁脉冲的非线性传输线关键技术。

基于非线性结构分析的架空输电线路风致位移响应研究

高压输电线路的稳定性和可靠性是影响电网安全稳定运行的重要因素。因此,开展输电塔线体系的风致响应研究,一直是输电工程技术领域的研究热点。以220 kV输电线路为例,进行了脉动风场的数值模拟,分析了塔线体系的振动形态,重点研究了风载荷作用下导线的振动形态以及在不同工况下由导线振动引起的位移变化。深入分析了输电线路的瞬态动力学响应,包括对架空输电线路的模态分析、风载荷下的振动过程以及不同工况下塔线的位移变化。结果表明:铁塔与导线的振动主要为一阶模态、二阶模态低频振动;导线的振动模式主要影响塔线体系的振动,不同时刻下振动位移的最大值对系统安全运行有更严重的影响。研究分析结果对输电线路的防风抗灾、安全稳定运行具有指导意义。

齿侧间隙非线性函数拟合阶次的选取研究

针对齿侧间隙非线性函数拟合阶次的选取问题,以斜齿轮传动系统为例,对齿轮系统进行了理论建模、仿真分析,并对实际齿轮系统进行了实验研究。首先,采用集中质量法建立了考虑轴向振动的齿轮非线性系统模型,并对数学模型进行了无量纲化,对齿侧间隙函数分别进行了无拟合、4阶拟合和8阶拟合处理;然后,采用Runge-Kutta数值积分法进行了数值仿真分析,得到了齿轮系统x、y、z三个方向的幅值-频率比响应曲线图,研究了拟合阶次对系统x、y、z三个方向动态特性的影响;最后,进行了齿轮系统动态测试,得到了齿轮系统x、y、z三个方向的振动响应图,根据仿真与实验结果得出了结论。研究结果表明:不同处理方式下的齿轮系统振动响应在z向的差异较大,拟合阶次的选取应重点考虑z向;在x、y方向,齿侧间隙非线性4阶拟合函数会提前改变齿面接触状态且共振振幅分别增大1倍和1/3倍;对于多间隙的齿轮非线性系统,对齿侧间隙进行无拟合处理,可能导致计算困难和结果不准确;在固有频率附近,对齿侧间隙进行4阶拟合处理能够最大程度弥补其他非线性因素带来的影响;在其他频率范围,对齿侧间隙进行8阶拟合处理会更接近真实齿轮系统。齿侧间隙非线性函数的拟合处理在提高了计算效率的同时,也提高了模型的准确性。

静止无功补偿器的新型最优非线性比例积分电压控制

针对传统PI应用于静止无功补偿器(static var compen-sator,SVC)这个非线性复杂系统上,所体现出的快速性与稳定性之间的矛盾,以及对精确数学模型的依赖性,适应性及鲁棒性较差,该文设计了以非线性函数与传统PI控制器串联起来构成非线性PI控制器,简单易于实现。并且提出基于改进的单纯形加速算法(simplex method,SPX),以时间乘以误差绝对值积分(integrate of time multiplied absolute error,ITAE)准则作为寻优目标函数,对非线性PI控制器的参数KP、KI进行实时调整、寻优,使SVC系统的瞬态响应过程达到最佳。仿真和实际应用结果表明该最优非线性PI控制器,不但能快速、无超调的跟踪SVC系统的电压设定值,而且可实现对无功功率、三相不平衡等多个因素的综合补偿,具有较强的鲁棒性、适应性和较高的补偿精度。

新型准零刚度隔振系统的设计与研究

通过并联具有负刚度特性的碟形弹簧与线性正刚度弹簧,设计了一种新型准零刚度隔振系统。通过静力学特性研究,建立了系统的力-位移和刚度-位移关系表达式,获取了系统在平衡位置具有准零刚度的参数条件;通过动力学特性研究,建立了系统分别在简谐力和简谐位移激励下的非线性动力学方程,应用平均法分析了系统参数和激励幅值对系统力传递率和位移传递率的影响,并与其等效线性系统进行了比较,证明了该系统在隔离低频和超低频振动时具有优异的隔振性能,为该新型准零刚度隔振系统的设计应用提供了理论指导。

非线性系统参数估计的一类有效搜索策略

结合模拟退火的随机概率突跳性搜索和单纯形法的凸多面体几何搜索 ,提出了非线性系统参数估计的一类有效搜索策略 .通过对多种非线性定常系统的多维参数估计和非线性时变水箱系统的参数与时滞在线联合估计的仿真研究 ,验证了该方法的可行性。

改进粒子群算法及其在输电网规划中的应用

根据粒子群算法收敛性受初始粒子分布影响较大的特点,结合非线性单纯体法(nonlinear simplex method NSM),提出了一种粒子群初始化方法。该方法克服了随机初始化粒子时不能保证粒子合理分布的缺点,对提高初始粒子质量、加速 PSO 算法的收敛速度起到了有效的作用;同时分析了罚函数形式的适应度函数使迭代过程产生振荡的现象,根据对偶拉格朗日法,提出了一种交叉迭代法,克服了罚函数法的不足。最后通过算例证明了这 2 种方法应用于电网规划的有效性和正确性,为 PSO 算法的进一步改进拓展了思路。

基于改进粒子群算法的输电网扩展规划

输电网扩展规划是一个非常复杂的大规模组合优化问题,提出了一种改进粒子群算法求解此类优化问题。该算法针对传统的粒子群算法存在的缺点,对粒子群迭代行动策略、初始化策略以及惯性权重的调整进行了改进,并将单纯形法引入到算法中,弥补算法容易陷入局部最优的缺点,提高了粒子群算法的搜索效率,使其更适用于输电网扩展规划。将其应用到Garver-6节点系统和一个18节点系统,计算结果证明该算法的可行性和有效性。

用透过率测试曲线确定半导体薄膜的光学常数和厚度

介绍了一种简单而准确地确定薄膜光学常数和厚度的方法 .借助于Forouhi Bloomer物理模型 ,用改进的单纯形法拟合分光光度计透过率测试曲线 ,获得半导体薄膜的光学常数和厚度 .对射频磁控溅射和直流反应溅射制备的玻璃基板上的α Si和ZnO薄膜进行了实验 ,拟合的理论曲线和实验曲线吻合得非常好 .计算得到的结果与文献报道的结果和台阶仪的测量结果一致 ,误差小于 4 % .该方法对无定形或多晶的半导体薄膜都适用 ,也可以用于计算厚度较薄的薄膜 .