受迫阻尼振动系统动力学性质的研究

对受迫阻尼振动系统3种情况的动力学行为以及它们的能量状况作了较深入的定量研究,该研究对分析我们遇到的实际受迫振动系统有一定的指导意义。     

关于弱阻尼自由振动能量及极值点相位的讨论

本在振动速度表达式的基础上，通过对弱阻尼自由振动能量和极值点相位的推导，得出振动能量和极值点相位的表达式不同于简谐振动，并与阻尼比有关的结论。     

一类线性阻尼振子的随机共振研究

针对随机有色噪声参数激励和周期调制噪声外激励联合作用下的线性阻尼振子,利用Shapiro-Loginov公式推导了系统响应的一、二阶稳态矩的解析表达式.发现这类系统存在传统的随机共振、广义的随机共振和“真正”的随机共振;当乘性噪声强度和调制噪声强度的比值大于等于1时,系统出现随机多共振现象.通过数值计算的系统响应功率谱,验证了理论分析结果. 关键词： 随机共振 周期调制的噪声 线性阻尼振子     

用钕铁硼制作阻尼振动、受迫振动及共振演示仪

利用稀土永磁性材料钕铁硼(Nd-Fe-B)设计制作出了新型阻尼振动、受迫振动及共振演示仪.该演示仪器可演示阻尼振动的3种状态(欠阻尼状态、临界阻尼状态、过阻尼状态)、受迫振动及共振现象.     

对称双弹簧振子受迫、有阻尼横振动的混沌行为

对受周期外力驱动的对称双弹簧振子进行了研究,建立了系统的动力学方程,用线性稳定性分析方法讨论了平衡点附近邻域的稳定性,利用数值计算并结合多种分析方法,求解非线性方程和判断解的性质.通过改变系统参数,画出时域图、相图及分岔图等.计算分析和数值实验发现,这个简单的力学系统存在十分丰富的动力学行为(分岔、混沌).理论分析和数值实验结果一致.     

A2B模型阻尼受迫振动方程组的通解

导出了A2B模型阻尼受迫振动方程组的通解,并讨论其算例和图像.     

Topological resonance energy,bond resonance energy,and circuit resonance energy

Circuit resonance energy (CRE) is a key quantity that links energetic and magnetic criteria of aromaticity for a polycyclic π‐system. Topological resonance energy (TRE) correlates well with the sum of CREs for an entire π‐system. We found that bond resonance energy (BRE), so far defined to estimate the degree of kinetic stability for a polycyclic π‐system, also correlates very well with the corresponding quantity defined with CREs. These findings justify the view that graph‐theoretical quantities, such as TRE and BRE, can be used safely even though they rely on unrealistic reference structures. Copyright © 2007 John Wiley & Sons, Ltd.     

Stochastic resonance of a damped oscillator with frequency fluctuation driven by a periodic external force

<正>Considering a damped linear oscillator model subjected to a white noise with an inherent angular frequency and a periodic external driving force,we derive the analytic expression of the first moment of output response,and study the stochastic resonance phenomenon in a system.The results show that the output response of this system behaves as a simple harmonic vibration,of which the frequency is the same as the external driving frequency,and the variations of amplitude with the driving frequency and the inherent frequency present a bona fide stochastic resonance.     

关于受迫振动、共振的实验研究

简要分析了现行中学物理课本中关于受迫振动和共振的演示实验中存在的缺点,并针对其不足加以改进.改进后的实验装置演示效果更好,便于学生理解和掌握相应的物理规律.     

Stochastic resonance in linear system driven by multiplicative and additive noise

The stochastic resonance (SR) is studied in an overdamped linear system driven by multiplicative and additive noise when the additive noise is a linear combination of an asymmetric dichotomous noise and its square. The exact expressions are obtained for the first two moments and the correlation function and the SR phenomenon appeared. There are three different forms of SR: the bona fide SR, the conventional SR and SR in the broad sense. Moreover, the asymmetry of multiplicative noise has different effect on signal-to-ratio (SNR) for the first two different forms of SR and the effects of multiplicative noise and additive noise on SNR are different.     

非平衡磁控溅射双势阱静电波动及其共振耦合

非平衡磁控靶表面电场和磁场相互正交构成磁阱结构,磁控靶和与之平行的偏压基片之间形成了另一种势阱结构,等离子体静电波动在这两种势阱结构中形成耦合共振.采用Langmuir探针研究等离子体中参数和浮置电位信号的功率谱密度.典型放电条件下两种势阱结构中的本征频率分别约为30—50 kHz和10—20 kHz,两种势阱条件下根据声驻波共振模式计算的电子温度数值与实验结果相符合.     

线性时滞反馈引起的周期性振动共振分析

研究了高频信号和微弱低频信号同时激励下线性时滞反馈对过阻尼双稳系统和Duffing振子系统中振动共振现象的影响. 解析分析和数值结果都表明, 系统对低频信号的响应幅值增益随时滞参数的变化同时呈现两种不同的周期性关系, 其周期分别为输入的高频信号和低频信号的周期. 数值结果还表明, 对不存在经典振动共振现象的单稳Duffing系统, 通过调节时滞参数也可以引发振动共振现象. 使用时滞反馈不仅可以有效地控制振动共振, 还可以进一步增强系统对微弱低频信号的响应. 关键词： 双稳系统 Duffing 系统 线性时滞反馈 振动共振