表面缺陷对波导丝中的扭转波传播影响研究

波导丝是磁致伸缩位移传感器的核心元件,其表面质量直接影响传感器的测量精度。为研究波导丝表面质量对检测信号的影响规律,通过建立扭转波在波导丝中传播的力学模型,得到扭转波的波动方程。在此基础上,对2种不同表面状况下波导丝中扭转波的传播开展数值模拟和实验验证。研究结果对今后高精度大量程磁致伸缩位移传感器的研制具有一定参考作用。     

位移法浅水波方程的解及其特性

不同于传统流体力学,在Lagrange坐标下推导浅水波方程.若将水平位移作为基本变量,则推导出的浅水波数学模型可描述为固体力学的非线性大位移问题.运用不可压缩条件,通过变分原理推导出位移法浅水波方程,给出椭圆函数形式的行波解,并分析孤波解产生的条件.该基础研究建立了在分析结构力学中分析浅水波问题的理论基础,有利于进一步开展水动力学的研究.     

扁锥面单层网壳的非线性动力学特性

用拟壳法建立了正三角形网格三向扁锥面单层网壳的轴对称非线性动力学基本方程．通过分离变量函数法,用Galerkin法得到了一个含二次、三次的非线性微分方程．为了研究混沌运动,对一类非线性动力系统的自由振动方程进行了求解,给出了单层扁锥面网壳非线性自由振动微分方程的准确解．通过求Melnikov函数,给出了发生混沌运动的临界条件．数字仿真证实了混沌运动的存在．     

近空间飞行器变增益非线性切换控制器设计

针对变后掠翼近空间飞行器大包络、多工作模态和模型不确定的特点,研究其模态切换过程中姿态的鲁棒跟踪控制问题.首先建立含扰动项的飞行器非线性切换模型,基于反步滑模方法和非线性干扰观测器设计鲁棒控制器,通过公共Lyapunov函数理论证明所设计的控制律能够保证闭环切换系统的稳定性;采用变增益切换控制策略为不同飞行模态设计合适的控制增益,用以提高系统的动态性能.仿真结果验证了所提出方法的有效性和必要性.     

一类Bent函数的二阶非线性度下界

为了防止存在有效的低次函数逼近,对于较小的正整数r,用于对称密码系统中的布尔函数应具有较高的r-阶非线性度.当r>1时,准确计算布尔函数的r-阶非线性度十分困难,已有的研究工作主要是通过分析其导函数的(r-1)-阶非线性度来确定布尔函数的r-阶非线性度下界.对于整数n≡2(mod 4),文中确定了一类由Niho指数生成的Bent函数的二阶非线性度下界.与相同变元个数的两类Bent函数和三类布尔函数相比,这类Bent函数具有更紧的二阶非线性度下界.     

微机械折叠波导慢波结构冷测特性的研究

在太赫兹频段,折叠波导行波管因其重要的应用价值已成为一个研究热点.介绍了折叠波导结构和折叠波导行波管,优化设计了一种560GHz行波管器件的结构尺寸,并分别用理论解析方法和软件模拟工具研究了折叠波导慢波结构的冷测特性.文章还对该类折叠波导慢波结构的微加工技术进行了初步的探讨,提出了基于ICP体硅深刻蚀、无电镀铜等组合工艺方案.     

变元可分离核函数对非线性支持向量分类机的影响

证明了变元可分离函数在Hilbert空间中满足Mercer定理的条件,为构造新的非线性支持向量分类机时选定核函数提供了一种新方法,并通过新方法构造的核函数与其它核函数构造的非线性支持向量分类机比较,得出了较好的结果。     

LiNbO3光波导紫外表面等离子共振传感器模拟计算

高折射率的LiNbO3光波导,构成四层高折射率波导表面等离子共振传感器.采用传输矩阵方法得基模TM模色散表达式,研究了光波导有效折射与样品折射率之间的关系、光波导传输常数和波长的关系,由表面等离子体波共振耦合条件,得到不同样品折射率的表面等离子共振波长.利用菲涅耳的反射率公式,计算了四层结构波导传感器的透射谱,得到表面...     

基于变尺度编码CMAC的增强学习控制器及其应用

研究了一种基于变尺度编码CMAC神经网络的增强学习控制器设计方法,并应用于以自行车平衡为模型的非线性随机系统的学习控制中.该方法通过对Markov决策过程状态空间的变尺度重叠量化编码,实现基于CMAC的多分辨率值函数逼近,从而有效地提高了增强学习控制器对连续状态空间马氏决策问题的泛化性能.针对自行车学习控制的仿真研究表明,采用变尺度编码CMAC进行值函数逼近的增强学习控制器能够获得优于已有表格型方法和均匀编码CMAC方法的学习效率和泛化性能.     

复模态分析超临界轴向运动梁横向非线性振动

近似解析研究了简支边界条件下超临界轴向运动梁横向非线性自由振动的固有频率和模态函数.采用复模态方法处理控制方程,一个积分偏微分方程.将Galerkin截断思想用于近似处理线性化方程,一个含空间依赖系数的常微分方程.给出了不同截断项数对固有频率的影响.基于8项截断,讨论了系统参数对模态函数的影响.     

N-solitons,breathers, lumps and rogue wave solutions to a (3+1)-dimensional nonlinear evolution equation

Based on Hirota bilinear method, $N$-solitons, breathers, lumps and rogue waves as exact solutions of the (3+1)-dimensional nonlinear evolution equation are obtained. The impacts of the parameters on these solutions are analyzed. The parameters can influence and control the phase shifts, propagation directions, shapes and energies for these solutions. The single-kink soliton solution and interactions of two and three-kink soliton overtaking collisions of the Hirota bilinear equation are investigated in different planes. The breathers in three dimensions possess different dynamics in different planes. Via a long wave limit of breathers with indefinitely large periods, rogue waves are obtained and localized in time. It is shown that the rogue wave possess a growing and decaying line profile that arises from a nonconstant background and then retreat back to the same nonconstant background again. The results can be used to illustrate the interactions of water waves in shallow water. Moreover, figures are given out to show the properties of the explicit analytic solutions.     

Statistical characteristics of anomalously large surface waves based on computational experiments

The computational experiments on modeling surface waves, which are used for studying the statistics of the occurrence of extremely large surface waves depending on the parameters of the initial waves, are considered. The sudden occurrence of abnormally large waves in the ocean is a big hazard for marine vessels and structures. In recent years, incontrovertible evidence of this phenomenon, such as instrumentation records and photographs, has been presented. The main method of studying the phenomenon of rogue waves in this work is computational experiments based on the complete nonlinear hydrodynamic equations of an ideal liquid with a free surface. The method of conformal variables that is used for the original system of equations enables one to make effective and accurate calculations by computers and computing complexes. According to the experimental results, the statistics of the occurrence of anomalously large surface waves is studied. The use of dissipation and pumping in these computational experiments has made it possible to perform continuous calculations that are not stopped if a rogue wave occurs. The intensity of the occurrence of rogue waves depending on the values of the squares of the mean steepness and wave dispersion is estimated. It is shown that doubling the computational region almost doubles the intensity. The proposed procedure of the computational experiments allows estimating the average waiting time of a rogue wave in the assigned region.     

Lax pair,Darboux transformation and Nth-order rogue wave solutions for a (2+1)-dimensional Heisenberg ferromagnetic spin chain equation

A new (2+1)-dimensional Heisenberg ferromagnetic spin chain equation is investigated, which can be used to describe magnetic soliton excitations in two dimensional space fields and a time field. The Lax pair of the equation is first constructed. Based on the Lax pair, initial seed solution and Darboux transformation, the analytic first-, second- and third-order rogue wave solutions are obtained, and a general expression of the $N$th-order ($N>3$) rogue wave solutions is presented. The impacts of the system parameters on the rogue waves are demonstrated through numerical visualization method.     

基于Matlab的越野汽车非线性悬架系统仿真

建立了考虑刚度和阻尼非线性的两自由度越野汽车悬架系统的仿真模型。用谐波叠加法构成的路面不平度作为路面激励,并利用半波正弦信号模拟越野汽车通过半圆形路障时的激励,在这些激励下,用数值方法获得了车身加速度,车轮动载,悬架动挠度的响应以及冲击作用下车身加速度的模拟响应。根据随机振动理论谱估计方法,由输入输出信号获得非线性悬架系统传递函数的数值解。以此为基础分析了非线性悬架系统在不同行驶工况下的表现出的传递特性的差异。     

A symbolic computation approach to constructing rogue waves with a controllable center in the nonlinear systems

A symbolic computation approach to constructing higher order rogue waves with a controllable center of the nonlinear systems is presented, making use of their Hirota bilinear forms. As some examples, it turns out that some higher order rogue wave solutions of the Kadomtsev–Petviashvili (KP) type equations in $(3+1)$ and $(2+1)$-dimensions are obtained. Some features of controllable center of rogue waves are graphically discussed.     

Rational and semi-rational solutions of the y-nonlocal Davey–Stewartson I equation

The nonlocal Davey–Stewartson (DS) I equation with a parity-time-symmetric potential with respect to the $y$-direction, which is called the $y$-nonlocal DS I equation, is a two-dimensional analogue of the nonlocal nonlinear Schrödinger (NLS) equation. The multi-breather solutions for the $y$-nonlocal DS I equation are derived by using the Hirota bilinear method. Lump-type solutions and hybrid solutions consisting of lumps sitting on periodic line waves are generated by long wave limits of the obtained soliton solutions. Also, various types of analytical solutions for the nonlocal NLS equation with negative nonlinearity, including both the Akhmediev breathers and the Peregrine rogue waves sitting on periodic line waves, can be generated with appropriate constraints on the parameters of the obtained exact solutions of the $y$-nonlocal DS I equation. Particularly, we show that a family of hybrid solitons describing the Peregrine rogue wave that coexists with the Akhmediev breather, both of them sitting on a spatially-periodic background can be thus obtained.     

非线性量化小脑模型关节控制器神经网络控制器

常规小脑模型关节控制器(CMAC)神经网络采用线性均匀量化,稳态控制精度与量化级数相关,增加量化级数可提高稳态精度但会导致内存空间和计算量的增加.本文提出一种可采用幂函数、高斯、分段3种非线性量化方法的非线性量CMAC神经网络,并分析了非线性量化CMAC的收敛性,解释了非线性量化提高稳态精度的本质.面向一阶惯性环节、二阶系统、一阶时变系统及二阶时变系统,分别跟踪方波、斜坡、正弦波、三角波和加速度等输入信号,仿真验证了非线性量化CMAC神经网络控制器的有效性,给出了不同非线性量化方法的适用性.结果表明,非线性量化CMAC参数容易设定,物理意义清晰,与常规CMAC对比,其快速性和控制精度显著提高,可以有效解决实际复杂非线性时变系统的控制.     

Numerical solution of potential flow equations with a predictor-corrector finite difference method

We develop a numerical solution algorithm of the nonlinear potential flow equations with the nonlinear free surface boundary condition.A finite difference method with a predictor-corrector method is applied to solve the nonlinear potential flow equations in a two-dimensional (2D) tank.The irregular tank is mapped onto a fixed square domain with rectangular cells through a proper mapping function.A staggered mesh system is adopted in a 2D tank to capture the wave elevation of the transient fluid.The finite difference method with a predictor-corrector scheme is applied to discretize the nonlinear dynamic boundary condition and nonlinear kinematic boundary condition.We present the numerical results of wave elevations from small to large amplitude waves with free oscillation motion,and the numerical solutions of wave elevation with horizontal excited motion.The beating period and the nonlinear phenomenon are very clear.The numerical solutions agree well with the analytical solutions and previously published results.     

谐波平衡法求解俯仰运动矩形贮箱中液体非线性晃动

针对俯仰运动贮箱中液体的晃动用变分原理建立了一类新的Lagrange函数,以此为基础可以解析方式来研究俯仰运动贮箱中液体的非线性晃动．首先将速度势函数Φ在自由液面处作波高函数叩的Taylor级数展开,从而导出自由液面运动学和动力学边界条件非线性方程组;然后用谐波平衡法(HBM)假设其解为各次主导谐波叠加的形式,并代入方程组中得到含有未知系数相应多个代数方程式;最后用Broyden法对代数方程组求解．以无挡板开口二维、刚性矩形贮箱为例,研究了液体的大幅晃动,就液体晃动的幅值而言,在一定激励频率范围内,理论计算值与试验结果吻合较好,同时液面波高出现明显的零点漂移现象．     

Exact analytic solitary wave solutions for the RKL model

Interest in finding exact solitary wave solutions of nonlinear evolution equations by means of different methods has grown steadily in recent years. These exact solutions are important to understand the mechanism of the complicated nonlinear physical phenomena. By use of the Jacobi elliptic function method, we find the exact analytic solitary wave solutions for the RKL model with cubic-quintic non-Kerr terms, describing the propagation of extremely short pulses in optical fibers. These new solutions may be useful for describing the propagation of optical pulses in non-Kerr media.