Probing nonlinear systems with the Wigner distribution

A new way to study nonlinear systems under forced oscillations is presented. The approach is based on the analysis of the time-frequency spectrum of the output signal of the nonlinear system when a chirp (a frequency increasing in time) is applied as input signal. The time-frequency spectrum is a way to characterize the instantaneous frequency content of a signal. In this paper it is shown that this approach gives a physical explanation of the mechanism that generates forced nonlinear oscillations. Results with simulated and real data prove the validity of the method.     

基于调频EMD的结构非线性辨识方法研究

提出了调频EMD方法,克服了原EMD方法在密集频率情况下容易产生固有模式函数(Intrinsic Mode Function,IMF)混淆的弱点,可以较好地分解相对密集频率的弱非线性信号,得到物理意义相对明确的IMF。与Hilbert-Huang变换相结合,有效地识别多自由度弱非线性系统瞬时模态信息的变化过程。通过数值仿真计算证明了调频EMD方法的有效性。利用调频EMD方法对Humber大桥的主梁两自由度节段模型自由气弹振动信号进行识别,揭示了该耦合系统的非线性。     

车辆通过连续减速带时的非线性振动特性分析

在7自由度线性系统的基础上考虑悬架弹簧、阻尼和轮胎的非线性,以高速路段的连续减速带作为整车激励,通过对力学模型进行分析并运用拉格朗日法建立系统微分方程。通过MATLAB仿真软件对整车7自由度非线性振动模型的微分方程进行仿真,得到阻尼非线性系数和激励频率的分岔图,发现在一定区域内系统出现复杂的非线性振动,并通过时间历程图、相位图、Poincare截面图和PSP峰值图深入研究系统的周期、拟周期和混沌运动,揭示出阻尼非线性系数和激励频率对系统振动的影响,最后通过拟合即时速度从变速的角度揭示减速车辆通过连续减速带时的振动情况。     

Resonance phenomena in the nonlinear vibration of plates governed by Duffing''s equation

This paper presents a theoretical and experimental study of the resonance phenomena of a nonlinear system, the time dependent part of which is governed by Duffing's equation. The method of Krylov, Bogoliubov and Mitropolsky is applied to analyze the transient motion near resonance, and the amplitude of the system is shown to change rapidly, during a short time duration, at certain critical driving frequencies. During this transitional period, the instantaneous response frequency of the system differs from the driving frequency, and the variation of amplitude vs response frequency is bounded by the usual steady-state nonlinear response curve. Experimental results are presented for a clamped circular plate driven into large amplitude oscillations by a magnetic force, during the downward and upward “jumps”. The transient nonlinear response curves during the jumps, and the free vibration (skelton) curves of the plate are determined experimentally. Methods for measuring the damping coefficient, linear frequency and nonlinear stiffness of the plate are also discussed.     

Introduction to the special issue on the 2011 Joint IEEE International Frequency Control Symposium and European Frequency and Time Forum

The 8 invited and 17 contributed papers in this special issue focus on the following topical areas covered at the 2011 Joint IEEE International Frequency Control Symposium and European Frequency and Time Forum, held in San Francisco, California: 1) Materials and Resonators; 2) Oscillators, Synthesizers, and Noise; 3) Microwave Frequency Standards; 4) Sensors and Transducers; 5) Timekeeping and Time and Frequency Transfer; and 6) Optical Frequency Standards.     

基于时滞惯性流形的浅拱动力屈曲研究

从动力学观点,浅拱受冲击是一种无穷维或者连续的动力系统,论文针对抛物线浅拱,应用有关薄壁结构的基本理论和非线性几何关系推导并建立其控制微分方程。然后,利用时滞惯性流形的思想,提出一种求解这类强非线性偏微分方程的新方法,即基于时滞惯性流形的非线性Galerkin方法。通过这种方法,把原始方程的解投影到由控制方程中线性算子的特征函数所张成的完备空间内,并构造出无限维子空间内的动力行为与有限维子空间内的动力行为之间的耦合作用,该耦合作用认为高低阶分量间的相互作用并不是一种简单的瞬时行为,而是与模态发展的历史有关。通过数值分析得到：系统存在两个稳定平衡位置,与传统的Galerkin方法相比,所提出的基于时滞惯性流形的非线性Galerkin方法可以大幅度地降低方程的维数,提高计算速度,有效地降低对计算机内存的需求和减少计算时间。某种程度上,时滞惯性流形为系统的非线性动力行为如屈曲、分岔、突跳等动态模拟和数值分析提供了一个新的更为合理的研究手段。     

Timing Traceability and the Link Between ISRO-NPLI

We present an algorithm for timescale prediction of IRNSS Network Time (IRNWT) using a GNSS link for daily exchange of data between Indian Space Research Organization and CSIR-NPL. A link between CSIR-NPL and IRNWT through Two Way Satellite Time and Frequency Transfer is also being established.     

Further Characterization of the Time Transfer Capabilities of Precise Point Positioning (PPP): The Sliding Batch Procedure

In recent years, many national timing laboratories have installed geodetic Global Positioning System receivers together with their traditional GPS/GLONASS Common View receivers and Two Way Satellite Time and Frequency Transfer equipment. Many of these geodetic receivers operate continuously within the International GNSS Service (IGS), and their data are regularly processed by IGS Analysis Centers. From its global network of over 350 stations and its Analysis Centers, the IGS generates precise combined GPS ephemeredes and station and satellite clock time series referred to the IGS Time Scale. A processing method called Precise Point Positioning (PPP) is in use in the geodetic community allowing precise recovery of GPS antenna position, clock phase, and atmospheric delays by taking advantage of these IGS precise products. Previous assessments, carried out at Istituto Nazionale di Ricerca Metrologica (INRiM; formerly IEN) with a PPP implementation developed at Natural Resources Canada (NRCan), showed PPP clock solutions have better stability over short/medium term than GPS CV and GPS P3 methods and significantly reduce the day-boundary discontinuities when used in multi-day continuous processing, allowing time-limited, campaign-style time-transfer experiments. This paper reports on follow-on work performed at INRiM and NRCan to further characterize and develop the PPP method for time transfer applications, using data from some of the National Metrology Institutes. We develop a processing procedure that takes advantage of the improved stability of the phase-connected multiday PPP solutions while allowing the generation of continuous clock time series, more applicable to continuous operation/ monitoring of timing equipment.     

Resonance oscillations of a gas in a shut-end tube in the region of transition to shock waves

The authors describe theoretical and experimental studies of resonance oscillations of a gas in a tube, with one end shut and a periodically vibrating piston mounted on the other. Analytical expressions to calculate the amplitude of pressure fluctuations in a real gas and experimental results at the frequency of linear resonance are obtained. Theory shows good agreement with experiment. An experimental study is made of nonlinear resonances of the second and third orders and the transition from almost harmonic oscillations of the gas to highly nonlinear ones. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 2, pp. 370–375, March–April, 2000.     

Improving Methods and Facilities for the Evaluation of Earth Orientation Parameters at the MMC SSTF

Measurement Techniques - The results of work carried out over the last five years to improve the methods and facilities of the Main Metrological Center of the State Service of Time, Frequency, and...     

Heat transfer during nonlinear oscillations of gas in a half-open tube

We present results of a study of heat transfer during nonlinear oscillations of a gas in a half-open tube.     

Internal energy flows and instantaneous field of a monochromatic paraxial light beam

It is known that the orbital angular momentum of a paraxial light beam is related to the rotational features of the instantaneous optical-frequency oscillation pattern within the beam cross section [J. Opt. A 11, 094004 (2009)]. Now this conclusion is generalized: any identifiable directed motion of the instantaneous two-dimensional pattern of the field oscillations ("running" behavior of the instant oscillatory pattern) corresponds to the transverse energy flow in the experimentally observable time-averaged field. The transverse orbital flow density can be treated as a natural geometric and kinematic characteristic of this running behavior.     

Nonstationary seismic response of a tank on a bilinear hysteretic soil using wavelet transform

A wavelet based nonlinear random vibration theory has been proposed in the present study to obtain responses of liquid storage tanks in form of instantaneous root mean square displacements of impulsive modes of the tank-liquid system supported on bilinear hysteretic (elasto-perfectly plastic) soil medium. The superstructure has been modeled by a combination of mass-spring-damper system. In order to evaluate the instantaneous root mean square values of the displacement responses of the tanks, zeroth moments of instantaneous power spectral density function (PSDF) have been evaluated. The hysteretic displacement is assumed to follow a truncated mixed Gaussian distribution. The evaluation of this zeroth moment depends on the post-yield or the pre-yield state of the hysteretic spring. The instantaneous root-mean-square (r.m.s) impulsive displacement response of the tank has been validated by simulation. A parametric study has been carried out to see the effects of the soil nonlinearity, the shear wave velocity in the soil and the height of the tank on tank responses.     

Nonlinear finite-volume time-domain analysis of photonic crystal-based resonant cavities

An accurate analysis of nonlinear photonic crystal (PhC) based resonant cavities is carried out. The nonlinearity considered for this analysis is a third-order nonlinearity with media composed of Kerr-like dielectric materials with an instantaneous nonlinearity. The analysis is performed with a robust and accurate finite-volume time-domain (FVTD) technique that for the first time has been extended in order to simulate nonlinear material with a Kerr-like instantaneous nonlinearity. From the analysis, interesting properties are revealed from the exploit of nonlinear characteristics of the PhC-based resonant cavities, properties that can be usefully applied for the realisation of all-optical circuits and specifically for optical switches.     

Wavelet analysis for gear crack identification

There are many typical damages and faults that can cause problems in relation to gear unit operation, a crack in the tooth root being probably the least desirable among them. It often results in failure of gear unit operation. Fault analyses presented in this article are based on gear units with real damages or faults, produced on the basis of real operating conditions. A test plant has been used. A possible damage can be identified by monitoring vibrations. The influences of a crack in a single-stage gear unit on produced vibrations are presented. A fatigue crack in the tooth root causes significant changes in tooth stiffness, whereas, in relation to other faults, changes of other dynamic parameters are more expressed. Different methods are used to analyse signals acquired by experiments. Signal analysis has been carried out in relation to a non-stationary signal, using the family of Time Frequency Analysis tools, such as Wavelets Analyses. Typical spectrogram and scalogram patterns resulting from reactions to faults or damages indicate the presence of damages in a very reliable way.     

Atomistic Simulation of the Explosion Welding Process

We study explosion welding process on the atomic level using molecular dynamics simulations. Our simulations show that jet formation—considered necessary for good bonding—is correlated with the instantaneous melting of the interface region. Moreover, we observe peeling off of material (up to 4 nm) from the bonded surfaces. Finally, the structure of the material immediately after the bonding process is observed to be nanocrystalline with crystal sizes of 10–20 nm.     

Static and dynamic forces on a permanent magnet levitating between superconducting surfaces

A charged magnetic microsphere (radius 100 µm) is levitating inside a superconducting niobium capacitor. Because of its charge of about 1 pC, oscillations about the equilibrium position can be excited and detected electrically. The properties of this oscillator are investigated in order to study the static and dynamic forces of magnetic levitation. We find resonance frequencies between 200 Hz and 600 Hz. The resonance frequency and the damping are amplitude dependent due to nonlinear return forces and nonlinear friction, respectively. At small amplitudes the Q value is about 10⁶ in vacuum. A dc field can be applied to change the equilibrium position and consequently the resonance frequency. From the data the spatial dependence of the static force and of the dynamic stiffness can be determined and an empirical relation between both is established. Quite often, we find a hysteretic behavior of the static force whereas the stiffness is a reversible function of the position. Amplitude dependent damping is observed both in the decay of the free oscillations and in the dependence of the amplitude of the forced oscillations on the driving force.     

污染扩散瞬态浓度场的非线性特征实验研究

为了探讨污染扩散瞬态浓度场是否具有非线性特征,利用基于数字图像处理技术和光学粒子散射理论的污染扩散瞬态浓度场光学测量系统,获得了污染扩散浓度场的二维时间和空间湍流信息,运用这些信息分析了分形和混沌等非线性特征,得出其嵌入维数为9,关联维数为3．218,Kolmogorov熵为0．138541,最大Lyapunov指数为0．63691。结果表明,污染扩散瞬态浓度场的瞬态浓度具有低维非线性特征,存在奇异吸引子,是混沌的。     

Dynamics of Tobacco Smoke under Resonant Oscillations in a Closed Tube

High Temperature - The dynamics of tobacco smoke is studied experimentally with nonlinear oscillations in a closed tube. The oscillations of a polydisperse gas suspension at a basic frequency are...     

H型断面渐近发散振动气动力特征的数值模拟研究

基于计算流体动力学(CFD)数值模拟和连续小波变换的方法研究了渐近发散振动条件下H型断面的非线性气动力。采用二维非定常不可压缩雷诺平均N-S方程结合重整化群(RNG)k-湍流模型计算纯扭转或竖向渐近发散振动条件下的气动力。采用复Morlet小波对气动力进行连续小波变换,结合蛇形罚函数方法提取小波脊。由小波脊识别气动力的各瞬时频率及对应的瞬时振幅。研究表明:H型断面在大振幅振动条件下的气动力存在多倍于强迫振动频率的高次谐波,各频率成份的瞬时振幅与激励瞬时振幅间存在复杂的非线性关系。