三自由度含间隙碰撞振动系统Neimark-Sacker分岔的反控制

分岔反控制作为传统分岔控制的逆问题, 其目的是在预先指定的系统参数点通过控制主动设计出具有所期望特性的分岔解. 以一类三自由度含间隙双面碰撞振动系统为研究对象, 在不改变原系统平衡解结构的前提下, 考虑到在碰撞振动系统反控制过程中由Poincaré映射的隐式特点和传统的映射Neimark-Sacker分岔临界准则带来的困难, 通过对原系统施加线性反馈控制器并利用不直接依赖于特征值计算的Neimark-Sacker分岔显式临界准则研究了此系统的分岔反控制问题. 首先对原系统施加线性反馈控制, 建立闭环控制系统的六维Poincaré映射. 由于六维映射的雅克比矩阵的特征值没有解析的表达式, 利用高维映射Neimark-Sacker分岔的显式临界准则, 获得了系统出现拟周期碰撞振动运动的控制参数区域. 然后采用中心流形-正则形方法分析了拟周期分岔解的稳定性. 数值仿真结果表明本文方法可以在指定的系统参数点通过控制设计出稳定的拟周期碰撞运动.     

Resonance response of a single-degree-of-freedom nonlinear vibro-impact system to a narrow-band random parametric excitation

The resonant response of a single-degree-of-freedom nonlinear vibro-impact oscillator with a one-sided barrier to a narrow-band random parametric excitation is investigated. The narrow-band random excitation used here is a bounded random noise. The analysis is based on a special Zhuravlev transformation, which reduces the system to one without impacts, thereby permitting the applications of random averaging over "fast" variables. The averaged equations are solved exactly and an algebraic equation of the amplitude of the response is obtained for the case without random disorder. The methods of linearization and moment are used to obtain the formula of the mean-square amplitude approximately for the case with random disorder. The effects of damping, detuning, restitution factor, nonlinear intensity, frequency and magnitude of random excitations are analysed. The theoretical analyses are verified by numerical results. Theoretical analyses and numerical simulations show that the peak response amplitudes will reduce at large damping or large nonlinear intensity and will increase with large amplitude or frequency of the random excitations. The phenomenon of stochastic jump is observed, that is, the steady-state response of the system will jump from a trivial solution to a large non-trivial one when the amplitude of the random excitation exceeds some threshold value, or will jump from a large non-trivial solution to a trivial one when the intensity of the random disorder of the random excitation exceeds some threshold value.     

Duffing单边碰撞系统的颤振分岔

针对碰撞系统中常见的颤振导致的彗尾碰撞问题,引入了彗尾映射的概念,提出了一种有效的研究碰撞系统中颤振现象的数值方法.并以典型的Duffing单边碰撞系统为例,研究了系统中的完全颤振和不完全颤振现象,同时分析了系统的颤振分岔.     

Lyapunov exponent calculation of a two-degree-of-freedom vibro-impact system with symmetrical rigid stops

A two-degree-of-freedom vibro-impact system having symmetrical rigid stops and subjected to periodic excitation is investigated in this paper. By introducing local maps between different stages of motion in the whole impact process, the Poincar'e map of the system is constructed. Using the Poincar'e map and the Gram-Schmidt orthonormalization, a method of calculating the spectrum of Lyapunov exponents of the above vibro-impact system is presented. Then the phase portraits of periodic and chaotic attractors for the system and the corresponding convergence diagrams of the spectrum of Lyapunov exponents are given out through the numerical simulations. To further identify the validity of the aforementioned computation method, the bifurcation diagram of the system with respect to the bifurcation parameter and the corresponding largest Lyapunov exponents are shown.     

Stochastic responses of Duffing–Van der Pol vibro-impact system under additive colored noise excitation

A response analysis procedure is developed for a vibro-impact system excited by colored noise. The non-smooth transformation is used to convert the vibro-impact system into a new system without impact term. With the help of the modified quasi-conservative averaging, the total energy of the new system can be approximated as a Markov process, and the stationary probability density function （PDF） of the total energy is derived. The response PDFs of the original system are obtained using the analytical solution of the stationary PDF of the total energy. The validity of the theoretical results is tested through comparison with the corresponding simulation results. Moreover, stochastic bifurcations are also explored.     

Open-loop frequency response for a chaotic masking system

In this paper, a new numerical simulation approach is proposed for the study of open-loop frequency response of a chaotic masking system. Using Chua's circuit and the Lorenz system as illustrative examples, we have shown that one can employ chaos synchronization to separate the feedback network from a chaotic masking system, and then use numerical simulation to obtain the open-loop synchronization response, the phase response, and the amplitude response of a chaotic masking system. Based on the analysis of the frequency response, we have also proved that changing the amplitude of the exciting (input) signal within normal working domain does not influence the frequency response of the chaotic masking system. The new numerical simulation method developed in this paper can be extended to consider the open-loop frequency response of other systems described by differential or difference equations.     

一类含非黏滞阻尼的Duffing单边碰撞系统的激变研究

以一类含非黏滞阻尼的Duffing单边碰撞系统为研究对象, 运用复合胞坐标系方法, 分析了该系统的全局分岔特性. 对于非黏滞阻尼模型而言, 它与物体运动速度的时间历程相关, 能更真实地反映出结构材料的能量耗散现象. 研究发现, 随着阻尼系数、松弛参数及恢复系数的变化, 系统发生两类激变现象: 一种是混沌吸引子与其吸引域内的混沌鞍发生碰撞而产生的内部激变, 另一种是混沌吸引子与吸引域边界上的周期鞍(混沌鞍)发生碰撞而产生的常规边界激变(混沌边界激变), 这两类激变都使得混沌吸引子的形状发生突然改变.关键词：非黏滞阻尼Duffing碰撞振动系统激变复合胞坐标系方法     

一类弹性和阻尼双分段非线性约束系统周期响应特性研究

考虑动态条件下的两种典型分段非线性约束, 根据广义耗散Lagrange原理建立一类具有弹性和阻尼双分段非线性约束系统动力学模型. 采用平均法求解得到系统在周期激励下的幅频响应关系. 分别比较系统在不同分段非线性约束条件下的时域响应、分岔响应和幅频响应, 得到受分段非线性约束的系统响应特性以及约束条件变化时系统响应的变化规律. 对比两种约束条件下的幅频响应, 研究得到系统稳定性受不同分段非线性因素影响及两种分段非线性约束之间的相互影响规律.     

CPT原子频标实验研究

介绍了相干布居囚禁（CPT）原子频标的小型、低功耗物理系统,并应用它开展实现了CPT原子频标的激光锁定、微波锁定方案的实验室研究.通过采用电流负反馈将激光频率锁定在原子对激光的吸收峰上,电压负反馈将微波频率锁定在电磁感应透明共振峰上,用该物理系统实现了闭环锁定的实验室桌面CPT频标实验系统.对该实验系统的频率稳定度测量获得200 s内优于5×10^-11τ^-1/2的结果.关键词：CPT原子频标频率稳定度激光稳频     

原子钟与相关物理学的研究

文章介绍了半个多世纪以来北京大学在原子钟与相关物理学研究方面的简况,其中包括光抽运碱金属汽室型、原子束型、激光抽运频率标准以及冷原子物理的研究.文章阐明了原子钟的基本工作原理、主要性能及其与各种物理因素的关系,叙述了提高汽室频标光抽运效率与降低各种频移和减少谱线增宽因素影响的方法.此外,还介绍了原子束频标中的Majorana跃迁研究、光抽运铯钟中解决长期工作与长期频率稳定度难题以及冷原子钟的一些设想等研究成果.     

一类非线性相对转动动力系统的平衡稳定性及组合谐波近似解

建立一类含广义非线性弹性力的两质量相对转动系统的非线性动力学方程. 应用变量梯度法构造李雅普诺夫函数,研究相对转动非线性自治系统的稳定性. 应用摄动法求得相对转动非线性非自治系统在两种不同频率谐波共同激励下的组合谐波响应的近似解.关键词：相对转动非线性动力系统稳定性组合谐波响应     

LLRF超导腔体控制系统的测试

中国科学院近代物理研究所自主研发的ADS注入器Ⅱ第一代高频低电平(LLRF)控制系统,工作频率为162.5 MHz;LLRF系统是由基于I/Q采样的正交解调技术构成的全数字闭环反馈控制系统,其主要功能是实现超导腔腔体电压幅值稳定控制、相位稳定控制与腔体谐振频率控制;LLRF控制系统在液氦温区超导腔上进行了系统稳定度和性能的在线测试,根据实验数据计算得超导腔体电压幅度稳定度为±3.4‰,相位稳定度为±0.3°,腔体表面峰值电场(Epk)能长时间稳定在25.1 MV/m。通过实验测试,检验了LLRF控制系统的性能,并对测试过程中出现的问题进行了分析,为将来超导腔LLRF控制系统运行积累了经验。     

光学系统受迫振动的激光测量方法

将激光信号与高帧频CCD结合,解决了光学系统中振动信号和激光信号之间的转换问题,不仅能够测量振动对系统光束指向稳定性的影响,而且能够得到振动信号本身的频率特性。利用该方法对振源为150 Hz和200 Hz两种条件下的光学系统受迫振动进行测量,得到了与输入信号相吻合的振动信号属性。通过实验与分析得知:时域振幅测量精度为6.25 m,频域分辨力为2 Hz,方法简便高效,测量结果准确,已应用于角多路准分子激光主振荡功率放大器系统打靶试验平台光束指向稳定性的研究中。     

Pulse and frequency response of a p-i-n photodiode with absorption layer fabricated in two-valley semiconductor

Starting from the transport equations of the phenomenological model for a two-valley semiconductor, we obtained the pulse response of a p-i-n photodiode with the absorption layer fabricated in a two-valley semiconductor (GaAs, InGaAs...). The pulse response was determined for the case when it was possible to linearize the transport equations. It was shown that the nonstationary effects influence significantly the intensity and speed of the response. The frequency response was obtained by applying the fast Fourier transform (FFT) to the pulse response.     

罗柯夫斯基线圈频率响应特性的测量方法

罗柯夫斯基线圈是测量陡脉冲电流的一种重要装置,其方波响应上升时间能达到纳秒量级,但是,它只能在一定频率范围内作线性测量。为了更好地分析罗柯夫斯基线圈测量灵敏度的频率特性,本文介绍了对西安交通大学研制的该线圈作的频率响应特性测定结果。 文中着重介绍了频响测量的点频法,并叙述了有关影响因素。例如:对信号源、标准电压表、匹配负载等一些专门要求。给出了实测曲线,还介绍了线圈本身各种集中参数的测量结果。     

具有二氧化硅温度补偿层的薄膜体声波谐振器的建模与分析（英）

薄膜体声波谐振器(FBAR)的谐振频率会受到外界环境温度的影响而产生漂移,对于FBAR滤波器而言,这种温度-频率漂移特性会导致其中心频率、插入损耗、带内纹波等性能发生变化,降低其在电学应用中的可靠性。应用ANSYS有限元分析软件,对一个典型Mo-AlN-Mo三层结构的FBAR进行了温度-频率漂移特性的仿真,得到其在［－50 ℃, 150 ℃］温度范围内的频率温度系数(TCF)约为－3510－6/℃。在FBAR叠层薄膜结构中添加了一层具有正温度系数的二氧化硅温度补偿层,分析了该补偿层厚度对FBAR的温度-频率漂移特性、谐振频率和机电耦合特性的影响。设计了具有一层二氧化硅温度补偿层的FBAR叠层,由Mo/AlN/SiO2/Mo多层薄膜构成,仿真得到其频率温度系数为0.87210－6/℃;与没有温度补偿层的FBAR相比,温度稳定性得以显著改善。关键词: Abstract: Key words:     

具有二氧化硅温度补偿层的薄膜体声波谐振器的建模与分析（英）

薄膜体声波谐振器(FBAR)的谐振频率会受到外界环境温度的影响而产生漂移,对于FBAR滤波器而言,这种温度-频率漂移特性会导致其中心频率、插入损耗、带内纹波等性能发生变化,降低其在电学应用中的可靠性。应用ANSYS有限元分析软件,对一个典型Mo-AlN-Mo三层结构的FBAR进行了温度-频率漂移特性的仿真,得到其在［－50 ℃, 150 ℃］温度范围内的频率温度系数(TCF)约为－3510－6/℃。在FBAR叠层薄膜结构中添加了一层具有正温度系数的二氧化硅温度补偿层,分析了该补偿层厚度对FBAR的温度-频率漂移特性、谐振频率和机电耦合特性的影响。设计了具有一层二氧化硅温度补偿层的FBAR叠层,由Mo/AlN/SiO2/Mo多层薄膜构成,仿真得到其频率温度系数为0.87210－6/℃;与没有温度补偿层的FBAR相比,温度稳定性得以显著改善。关键词: Abstract: Key words: