利用Duffing系统的同步识别信号中的微小差别

对于非线性Duffing方程,建立了相应的派生系统,证明了派生系统可以与原Duffing系统实现完全同步.通过同步,可以识别出激振信号中的微小差别.在实际仿真计算中,在系统出现混沌运动时,对于相同的激振信号,会出现同步;对于有很小差别的信号,不会出现同步.在拟周期激励时,信号的振幅有微小差别也不会出现同步.计算结果证明了此方法的有效性. 关键词： 非线性系统 同步 信号     

一类时变非线性振动系统的同步控制方法

对于一类非自治的非线性振动系统，设计了控制方法并建立了相应的派生系统，使得派生系统能与原系统达到同步.利用Lyapunov稳定性理论证明了两个系统在一定条件下可以达到同步，给出了耦合参数的选择条件.对于含参数激励与强迫激励的Mathieu方程以及拟周期激励的Duffing方程进行了实际的仿真计算，证明了派生系统可以与原系统的拟周期、混沌运动快速实现同步. 关键词： 派生系统 同步 差别方程     

非线性振动系统的预测同步方法研究

对于非线性振动系统,如果通过线性耦合可以实现派生系统与原系统的同步,则可以建立相应的预测派生系统,使得预测派生系统的响应与经τ时间以后的原系统响应同步,实现对原振动系统的非线性响应,特别是混沌响应的预测.也可以建立多级的预测派生系统,预测较长一段时间以后的振动系统未来的非线性响应.对于Duffing系统建立了6级的预测派生系统,可以比较精确地预测3s左右的原系统混沌响应. 关键词： 预测同步 派生系统 响应     

用激光自混合干涉测量扬声器的Q值

用激光自混合干涉方法测量扬声器振动,从扬声器振动引起的自混合干涉信号测量扬声器振动速率.由正弦波激振扬声器测量振速的幅频特性曲线,谐波中包含扬声器谐振频率的方波激振扬声器测量振速衰减曲线,分别按谐振法和衰减法测量得到扬声器的品质因数约13.3和10.2.由于方波激励时扬声器有谐波振动成分,由方波激励获得的衰减曲线测量得...     

结构振动模态声辐射理论及试验研究

从结构振动声辐射的一般规律、自由声场的声功率辐射理论和结构振动模态原理入手,对结构振动模态的声辐射与外加激励、模态参数之间的关系进行了理论推导和研究,得到,当激振点不变,振动模态辐射的平均声压级的变化量与激振力级的变化量之比为1;若激振力不变,任意两点处激振振动模态辐射的平均声压级的变化量与相应点振型元素级的变化量之比为1.对以上结果试验验证表明:理论值与实测值基本相符.     

激振摆参数振动的实验研究

研究了一种激振摆参数振动的实验.当激振频率为激振摆固有频率2倍时激振摆会产生共振.实验探讨了激振摆从微阻尼振动到共振的幅时特性和幅频特性.对于小振幅纵向激振,当激振频率接近激振摆固有频率2倍时,激振摆的摆幅对激振频率很敏感,在减小频宽数使激振摆振动接近共振的过程中,激振摆的摆幅数随时间数会震荡变化(类似"拍"现象),"拍"的周期数和峰谷差数都随频宽数减小而增加;"拍"现象消失后继续减小频宽数,摆幅数随时间数将持续指数增大,运动失稳;在频宽数为零时,摆幅数随时间数增加最剧烈,即共振发生.通过激振摆理论模型对实验结果进行了动力学分析,非线性动力学方程的数值解结果与实验结果吻合较好.该实验研究对于解决与共振相关的问题有潜在的应用价值.     

非线性磁式压电振动能量采集系统建模与分析

为便于评价、优化磁式压电振动能量采集系统的性能,系统研究了该类系统的建模与分析方法,建立了非线性的分布参数模型用于描述系统的非线性动力学行为,并采用谐波平衡法给出了谐波响应的解析解.随后利用仿真模型分析了磁铁间距、加速度幅值、负载阻抗对输出功率的影响,比较了不同激励频率和加速度幅值下的最优阻抗.结果表明:双稳态特性适用于低强度的振动环境,且愈接近临界区域,输出功率愈高,而单稳态渐硬特性适用于高强度振动环境,其最优间距并不靠近临界区域;阱间大幅运动和阱内小幅运动均存在高低能量态共存的现象,愈接近临界区域,现象愈明显;激振频率是影响最优负载阻抗的决定性因素.     

磁铁式弦振实验仪的研制

介绍了磁铁式弦振实验仪的测量机理和信号处理方法.在激振信号作用下,磁铁式弦振传感器的钢弦因受洛伦兹力而变形并作横向振动,利用电磁感应原理得到同频率的感应电势,根据钢弦振动的频率可算出传感器受力和变形.     

超混沌系统的广义同步化

研究了超混沌系统的广义同步化问题.基于Lyapunov稳定性理论，提出了一种新的线性及非线性广义同步方案，并从理论上证明了该方案的可行性.该方案不仅可以实现相同维数超混沌系统之间的广义同步，而且对于不同维数的系统之间的广义同步问题同样适用.合理地构造误差增益矩阵，即可实现驱动系统和响应系统之间的广义同步.数值模拟实验进一步验证了所提方案的有效性.     

四分之一波长喇叭式集中变幅杆构成的超声振动刀具系统

将超声波变幅杆与弯曲振动刀杆作为一个系统加以研究.通过对四分之一波长喇叭式集中变幅杆激振弯曲振动刀杆时理论分析和试验发现,该刀具系统中的变幅杆和弯曲振动刀杆虽然可以单独设计,但是应当按节点激振方式工作.     

Friction phenomena in a two-dimensional Frenkel-Kontorova model

By using the molecular dynamic simulation method with a fourth-order Runge--Kutta algorithm, a two-dimensional dc- and ac-driven Frenkel--Kontorova (FK) model with a square symmetry substrate potential for a square lattice layer has been investigated in this paper. For this system, the effects of many different parameters on the average velocity and the static friction force have been studied. It is found that not only the amplitude and frequency of ac-driven force, but also the direction of the external driving force and the misfit angle between two layers have some strong influences on the static friction force. It can be concluded that the superlubricity phenomenon appears easily with a larger ac amplitude and lower ac frequency for some special direction of the external force and misfit angle.     

Amplitude reduction of parametric resonance by dynamic vibration absorber based on quadratic nonlinear coupling

The paper proposes an amplitude reduction method for parametric resonance with a new type of dynamic vibration absorber utilizing quadratic nonlinear coupling. A main system with asymmetric nonlinear restoring force and harmonic excitation causes parametric resonance in the system. In contrast with autoparametric vibration absorber, the natural frequency of the vibration absorber is tuned to be in the neighborhood of twice that of the main system. For such a vibration absorber, we investigate the effect on the amplitude reduction for a parametrically excited main system. Analytical results using the method of multiple scales show that the amplitude of parametric resonance is reduced by the effect of the vibration absorber. The experimental results by a simple apparatus indicate that the parametric resonance is stabilized by the effects of both vibration absorber and Coulomb friction of the main system. Moreover, numerical results considering the Coulomb friction of the main system show that the amplitude of parametric resonance becomes close to zero by the proposed vibration absorber.     

H-infinity optimization of a variant design of the dynamic vibration absorber—Revisited and new results

The H_∞ optimum parameters of a dynamic vibration absorber (DVA) with ground-support are derived to minimize the resonant vibration amplitude of a single degree-of-freedom (sdof) system under harmonic force excitation. The optimum parameters which are derived based on the classical fixed-points theory and reported in literature for this non-traditional DVA are shown to be not leading to the minimum resonant vibration amplitude of the controlled mass. A new procedure is proposed for the H_∞ optimization of such a dynamic vibration absorber. A new set of optimum tuning frequency and damping of the absorber is derived, thereby resulting in lower maximum amplitude responses than those reported in the literature. The proposed optimized variant DVA is also compared to a ground-hooked damper of the same damping capacity of the damper in the DVA. It is proved that the proposed optimized DVA has better suppression of the resonant vibration amplitude of the controlled system than both the traditional DVA and also the ground-hooked damper if the proposed design procedure of the variant DVA is followed.     

Vibration analysis of a continuous system subject to generic forms of actuation forces and sensing devices

This work provides a general formulation to solve vibration problems for continuous systems with damping effects, including modal, transient, harmonic and spectrum response analyses. In modal analysis, the system eigenvalues and corresponding eigenfunctions can be determined. The orthogonal relations of eigenfunctions are shown. For transient, harmonic and spectrum analyses, the generic force/actuator functions and response/sensing operators are introduced, respectively, and used to derive the system response. The time domain response is obtained for transient analysis, the frequency response function is derived for harmonic analysis and statistical quantities of response variables due to random excitation are determined in spectrum analysis. The solution for each type of analysis can be formulated and expressed in a concise format in terms of generic force/actuator and response/sensor mode shape functions. In particular, one-dimensional beam and two-dimensional plate vibration analyses are illustrated by following the developed generic formulation. This work provides the complete analytical solutions of four types of vibration analyses for continuous systems and can be applied to other engineering structures as well.     

外力驱动下耦合弹簧振子的法诺共振

法诺共振是物理体系中普遍存在的一种非对称共振现象,它最早起源于量子物理,其微观图像是原子谱线中窄的分离态与宽的连续态之间的相干干涉.本文利用经典力学体系中两个弹簧振子的耦合,使其中一个弹簧振子受到周期性外力的驱动,成功类比了量子力学中的法诺共振现象.通过分析每个弹簧振子的动力学方程,严格求解它们的振动公式,从而得到每个...     

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.     

Large amplitude vibration of an initially stressed cross ply laminated plates

In this paper, nonlinear equations of large amplitude vibration for a laminated plate in a general state of nonuniform initial stress are derived. The equations include the effects of transverse shear and rotary inertia. Using these derived governing equations, the large amplitude vibration behaviour of an initially stressed cross-ply laminated plate is studied. The initial stress is taken to be a combination of pure bending stress plus an extensional stress in the plane of the plate. The Galerkin method is used to reduce the governing nonlinear partial differential equations to ordinary nonlinear differential equations and the Runge-Kutta method is used to obtain the nonlinear to linear frequencies. The frequency responses of nonlinear vibration are sensitive of the vibration amplitude, aspect ratio, thickness ratio, modulus ratio, stack sequence, layer number and state of initial stresses. The effects of various parameters on the large amplitude free vibrations are presented.     

旋转超声磨削平行砂轮复合变幅器设计与试验

为了获得大负载平行砂轮复合变幅器的设计方法,将复合变幅器简化为复合变幅杆与多阶环盘组成.利用Mindlin中厚板理论,求解了各振动环盘的位移、转角、弯矩和剪力解析表达式,通过复合变幅杆各振动单元间的力、位移的边界条件和连续条件,以及复合变幅杆和环盘两者结构间力与位移的耦合条件,建立了复合变幅器的数学模型和频率方程.针对...     

Experimental Investigation of Nonlinear Vibration Isolator with Fluidic Actuators (NLVIFA)

This paper elaborates a nonlinear fluidic low frequency vibration isolator designed with the characteristics of quasi-zero stiffness (QZS). The existing model of QZS vibration isolator enhances amplitude of vibration and attenuating vibration frequencies. This concern with displacement plays a vital role in the performance and instability of oblique spring setup reduces the isolator performance in horizontal non-nominal loads, in this accordance; this paper associates double acting hydraulic cylinder (fluidic actuators in short) in oblique and helical coil spring. An approximate expression of unique analytical relationship between the stiffness of vertical spring and bulk modulus of the fluid is derived for Quasi – Zero Stiffness Non-Linear Vibration Isolator with Fluidic Actuators (NLVIFA in short) system and the force transmissibility is formulated and damping ratio are discussed for characteristic analysis. Modal analysis carried out and compared with analytical results and an experimental prototype is developed and investigated. The performance of the NLVIFA reduces the external embarrassment more at low frequencies and the series of experimental studies showing that the soft nonlinearity causes limitation in the resonant frequency thereupon the isolation will be enhanced and NLVIFA greatly outperform some other type of nonlinear isolators.