双稳态结构中的1/2次谐波共振及其对隔振特性的影响

以典型的双稳态系统——屈曲梁结构为例,基于等效模型,结合解析、数值和实验手段,研究了双稳态结构中的1/2次谐波共振特性、演化过程、参数调节规律及其对隔振特性的影响.研究发现,当非线性刚度系数或激励幅值增加到一定程度时,系统会在一定带宽下产生显著的1/2次谐波共振;随着激励幅值增加,阻尼系统的1/2次谐波遵循“产生-增强-衰退-消失”的过程,该过程对峰值频率和峰值传递率有重要影响;适当提高非线性强度能有效改善双稳态结构隔振特性.针对双稳态屈曲梁结构开展的实验验证了1/2次谐波特性和隔振特性变化规律.     

Nonlinear dynamics of a pipe conveying pulsating fluid with combination,principal parametric and internal resonances

Nonlinear dynamics of a hinged–hinged pipe conveying pulsatile fluid subjected to combination and principal parametric resonance in the presence of internal resonance is investigated. The system has geometric cubic nonlinearity due to stretching effect out of immovable support conditions at both ends. The pipe conveys fluid at a velocity with a harmonically varying component over a constant mean velocity. For appropriate choice of system parameters, the natural frequency of the second mode is approximately three times that of the first mode for a range of mean flow velocity, activating a three-to-one internal resonance. The analysis is carried out using the method of multiple scales by directly attacking the governing nonlinear integro-partial-differential equations and the associated boundary conditions. The set of first-order ordinary differential equations governing the modulation of amplitude and phase is analyzed numerically for combination parametric resonance and principal parametric resonance. Stability, bifurcation and response behavior of the pipe are investigated. The amplitude and frequency detuning of the harmonic velocity perturbation are taken as the control parameters. The system exhibits response in the directly excited and indirectly excited modes due to modal interaction. Dynamic response of the system is presented in the form of phase plane trajectories, Poincare maps and time histories. A wide array of dynamical behavior is observed illustrating the influence of internal resonance.     

一类五次方振子系统的叉形分叉及振动共振研究

研究了一类具有分数阶导数阻尼的五次方振子系统中的叉形分叉及振动共振现象. 基于快慢变量分离法, 消去系统中的高频激励成分, 得到关于慢变量的等效系统, 根据等效系统中稳态平衡点的变化情况研究了系统的叉形分叉现象. 结果表明: 高频信号幅值的递增变化会引起亚临界叉形分叉, 高频信号频率和分数阶导数阻尼阶数的递增变化都会引起超临界叉形分叉; 振动共振和叉形分叉是关联的, 当叉形分叉发生时, 振动共振曲线会出现两个峰值, 否则只会出现一个峰值. 通过解析结果和数值模拟结果的对比, 验证了解析分析的正确性. 关键词： 亚临界叉形分叉 超临界叉形分叉 分数阶导数阻尼 振动共振     

可调谐二极管激光吸收光谱技术参数选择及优化

可调谐二极管激光吸收光谱技术(TDLAS)系统性能受调制参数,如调制度、调制频率、扫描幅度及扫描频率影响,实际测量中各参数不存在明确的选择依据。针对此问题,文章在一定的理论基础上通过实验分别观察各调制参数对二次谐波信号的影响,通过分析检测信号的特征,如幅值、信噪比、对称性及峰宽得出其变化规律,总结出在不同系统功能和需求下系统各调制参数的优化依据及方法。系统在计算浓度和温度时应优先考虑幅值和信噪比,从而使调制度达到最佳值,调制频率和扫描频率取较小值;在线形推导压强时优先考虑信号的对称性和峰宽,根据计算的具体要求确定调制参数;扫描幅度的确定以得到完整谐波信号为准;再根据系统的速度和精度需求调整扫描频率。该研究为此类系统工作状态的确定提供了实验依据。     

Analysis of the photon–photon resonance influence on the direct modulation bandwidth of dual-longitudinal-mode distributed feedback lasers

The paper explores the possibilities to extend the direct modulation bandwidth in dual-longitudinal-mode distributed feedback lasers by exploiting the photon–photon resonance induced by the interaction of the two modes in the laser cavity. The effects on the direct amplitude modulation and on the direct modulation of the difference frequency between the two modes are analyzed using simulation and experimental results. When the photon–photon resonance, which occurs at the difference frequency between the two modes, is properly placed at a higher frequency than the carrier-photon resonance, the small-signal amplitude modulation (AM) bandwidth of the laser can be significantly increased. However, both simulations and experiments point out that a high small-signal AM bandwidth does not lead to a high large-signal AM bandwidth if the small-signal modulation response has significant variations across the modulation bandwidth. The paper shows that a high large-signal AM bandwidth is obtained when the two modes are significantly unbalanced, whereas a high-bandwidth difference frequency modulation can be best detected when the two modes are balanced and the DC bias is properly chosen.     

Nonequilibrium dynamics of parametrically excited cold atoms via magnetic field-gradient modulation

We propose that the driven cold atomic system whose trap potential is periodically perturbed via parametric modulation of the magnetic field-gradien is a novel system to investigate the complex dynamics in nonlinear dynamical systems. We calculate the atomic trajectories and basins of attraction by varying the modulation amplitude and the modulation frequency. The calculation results show parametric resonance similar to those in Kim et. al.'s work [Opt. Commun. 236 (2004) 349] on cold atoms under parametric modulation of trap laser intensities in the case of small modulation amplitude or low modulation frequency. As the modulation amplitude or the modulation frequency is increased, the nonlinear effects are enhanced so that the dynamics of the system shows a wide variety of nonlinear behaviors, such as period doubling and chaos. We experimentally demonstrate the parametric resonance when the magnetic field gradient is parametrically modulated, which evidences the realization of the proposed system. We expect that this system is useful for understanding the stochastic phenomena occurring between complex basins of attraction, such as fluctuation induced transitions across the complex basin boundaries.     

有界噪声激励下带有时滞反馈的随机Mathieu-Duffing系统的响应

研究了参数激励下带有时滞反馈的随机Mathieu-Duffing方程的主参数共振响应问题.运用多尺度方法分离了系统的快慢变量.分析了系统的分岔性质,发现调谐参数、时滞、时滞项的系数以及非线性项的强度等都可以影响系统的分岔行为,适当选择这些参数可以改变系统的分岔响应.同时,还讨论了非零解的稳定性,得到了非零解稳定的充要条件,而且发现在随机激励的带宽较小时,系统的多解现象仍然存在,分岔和跳跃现象仍会发生,数值模拟验证了理论推导的有效性. 关键词： 随机Mathieu-Duffing系统 多尺度 稳定性 分岔     

Entropic bona fide stochastic resonance with periodic modulation

In this paper, we study the stochastic resonance (SR) in a geometrically confined system, where the irregular boundaries yield entropic barriers. When the boundaries are subjected to periodic modulation, the output signal-to-noise ratio (SNR) is calculated. The effects of the noise strength, the strength of the transversal force, the frequency and strength of modulation of the walls of the enclosure are discussed. Our results show that: (i) it is interesting to observe a resonance peak in the SNR as a function of the frequency of modulation, and therefore to the appearance of the entropic bona fide SR phenomenon; and (ii) the resonance peak is more pronounced with decreasing strength of the transversal force and increasing strength of modulation.     

窄带随机噪声作用下单自由度非线性干摩擦系统的响应

研究了单自由度非线性干摩擦系统在窄带随机噪声参数激励下的主共振响应问题.用Krylov-Bogoliubov平均法得到了关于慢变量的随机微分方程.在没有随机扰动情形,得到了系统响应幅值满足的代数方程.在有随机扰动情形,用线性化方法和矩方法给出了系统响应稳态矩计算的近似计算公式.讨论了系统阻尼项、非线性项、随机扰动项和干摩擦项等参数对于系统响应的影响.理论计算和数值模拟表明,当非线性强度增大时系统的响应显著变小,系统分岔点滞后;随着激励频率的增大系统响应变大,而当激励频率小于一定的值时,系统响应为零;增加干 关键词： 单自由度非线性干摩擦系统 主共振响应 Krylov-Bogoliubov平均法     

Bifurcation magnetic resonance in films magnetized along hard magnetization axis

We study low-frequency ferromagnetic resonance in a thin film magnetized along the hard magnetization axis performing an analysis of magnetization precession dynamics equations and numerical simulation. Two types of films are considered: polycrystalline uniaxial films and single-crystal films with cubic magnetic anisotropy. An additional (bifurcation) resonance initiated by the bistability, i.e. appearance of two closely spaced equilibrium magnetization states is registered. The modification of dynamic modes provoked by variation of the frequency, amplitude, and magnetic bias value of the ac field is studied. Both steady and chaotic magnetization precession modes are registered in the bifurcation resonance range.     

Parametric excitation of two internally resonant oscillators

The response of two-degree-of-freedom systems with quadratic non-linearities to a principal parametric resonance in the presence of two-to-one internal resonances is investigated. The method of multiple scales is used to construct a first-order uniform expansion yielding four first-order non-linear ordinary differential (averaged) equations governing the modulation of the amplitudes and the phases of the two modes. These equations are used to determine steady state responses and their stability. When the higher mode is excited by a principal parametric resonance, the non-trivial steady state value of its amplitude is a constant that is independent of the excitation amplitude, whereas the amplitude of the lower mode, which is indirectly excited through the internal resonance, increases with the amplitude of the excitation. However, in addition to Poincaré-type bifurcations, this response exhibits a Hopf bifurcation leading to amplitude- and phase-modulated motions. When the lower mode is excited by a principal parametric resonance, the averaged equations exhibit both Poincaré and Hopf bifurcations. In some intervals of the parameters, the periodic solutions of the averaged equations, in the latter case, experience period-doubling bifurcations, leading to chaos.     

Parametric resonance and cooling on an atom chip

This paper observes the parametric excitation on atom chip by measuring the trap loss when applying a parametric modulation. By modulating the current in chip wires, it modulates not only the trap frequency but also the trap position. It shows that the strongest resonance occurs when the modulation frequency equals to the trap frequency. The resonance amplitude increases exponentially with modulation depth. Because the Z-trap is an anharmonic trap, there exists energy selective excitation which would cause parametric cooling. We confirm this effect by observing the temperature of atom cloud dropping.     

频率变化的光场对双J-C模型中原子-原子纠缠的调控

本文研究了频率随时间变化的光场对双J-C模型中原子--原子纠缠的动力学调控, 主要讨论了光场频率随时间作正弦变化和脉冲变化两种典型情况下, 原子--原子纠缠度随时间的演化特性. 当光场频率随时间作正弦变化时, 原子--原子纠缠度演化的周期、振幅与光场频率调制的振幅有关, 并随着调制振幅的增强而减小. 光场频率的正弦调制和脉冲调制均能使光场与原子的相互作用模式在共振和非共振之间发生变化, 直接影响原子--原子纠缠度的演化规律. 通过光场频率的调制可以实现原子--原子纠缠度的提高与稳定, 避免ESD现象的出现, 从而达到动态调控原子--原子纠缠的目的.     

Modified rate equation model including the photon�Cphoton resonance

We show that, when the longitudinal confinement factor in an edge-emitting laser is treated as a dynamic variable, the modulation transfer function has an extra term. This term produces a supplementary photon?Cphoton resonance peak in the modulation response at a frequency corresponding to the frequency separation between longitudinal modes, when these modes are phase-locked long enough (quasi-phase-locked). The photon?Cphoton resonance peak is strongest when two consecutive quasi-phase-locked dominant longitudinal modes have similar longitudinal envelopes and share equally the photon population.     

Novel vibrational resonance in multistable systems

We investigate the role of multistable states on the occurrence of vibrational resonance in a periodic potential system driven by both a low-frequency and a high-frequency periodic force in both underdamped and overdamped limits. In both cases, when the amplitude of the high-frequency force is varied, the response amplitude at the low-frequency exhibits a series of resonance peaks and approaches a limiting value. Using a theoretical approach, we analyse the mechanism of multiresonance in terms of the resonant frequency and the stability of the equilibrium points of the equation of motion of the slow variable. In the overdamped system, the response amplitude is always higher than in the absence of the high-frequency force. However, in the underdamped system, this happens only if the low-frequency is less than 1. In the underdamped system, the response amplitude is maximum when the equilibrium point around which slow oscillations take place is maximally stable and minimum at the transcritical bifurcation. And in the overdamped system, it is maximum at the transcritical bifurcation and minimum when the associated equilibrium point is maximally stable. When the periodicity of the potential is truncated, the system displays only a few resonance peaks.     

Influence of the Magnetic Field Modulation on the Absorption Signal in an NMR Peak Flow Meter

The influence of the parameters of the magnetic field modulation in the analyzer of an NMR peak flow meter with flowing fluid on the magnitude and shape of the read-out signal in the mode with the modulation amplitude being much greater than the width of the resonance line is analyzed. Correlation factors are determined for the measured amplitude of the detected signal and for the duration of the magnetic mark in relation to the parameters of the magnetic field modulation in the analyzer and to the flow rate of the flowing fluid.     

基于广义局部频率的Duffing系统频域特征分析

针对传统功率谱在频率概念上的局限性及傅氏变换的固有缺陷, 提出一种新的广义局部频率概念,在自适应峰值分解方法的基础上, 研究周期激励下Duffing系统随阻尼参数r变化的频域动力学特征,发现了频率分岔现象, 并且不同参数r下的混沌时间序列在中心频率附近出现连续频段, 其形状具有相似性.通过厄米解调分析,总结出混沌时间序列具有频率调制特性和频率调制的相似性. 上述研究表明:提出的基于自适应峰值分解的广义局部频率方法, 能够有效提取Duffing系统的频域特征,为观察非线性系统混沌状态下频率连续分布规律提供一种新方法.     

Monte Carlo Simulation of Cooling Induced by Parametric Resonance

We demonstrate that the parametric resonance in a magnetic quadrupole trap can be exploited to cool atoms by using Bird＇s method. In our programme the parametric resonance was realized by anisotropically modulating the trap potential. The modulation frequency dependences of temperature and fraction of the trapped atoms are explored. Furthermore, the temperature after the modulation as functions of the modulation amplitude and the mean elastic collision time are also studied. These results are valuable for the experiment of parametric resonance in a quadrupole trap.     

Hexagonal Standing-Wave Patterns in Periodically Forced Reaction-Diffusion Systems

The periodically forced spatially extended Brusselator is investigated in the oscillating regime. The temporal response and pattern formation within the 2：1 frequency-locking band where the system oscillates at one half of the forcing frequency are examined. An hexagonal standing-wave pattern and other resonant patterns are observed. The detailed phase diagram of resonance structure in the forcing frequency and forcing amplitude parameter space is calculated. The transitions between the resonant standing-wave patterns are of hysteresis when control parameters are varied, and the presence of multiplicity is demonstrated. Analysis in the framework of amplitude equation reveals that the spatial patterns of the standing waves come out as a result of Turing bifurcation in the amplitude equation.