Self-excited oscillation under nonlinear feedback with time-delay

Several important applications use nonlinear feedback methods for synthetically inducing self-excited oscillations in mechanical systems. The van der Pol and saturation function type feedback methods are widely used. The effects of time-delay on the self-excited oscillation of single and two degrees-of-freedom systems under nonlinear feedback have been studied in this paper. It is shown that a single degree-of-freedom oscillator with the van der Pol type nonlinear feedback can produce unbounded response in presence of time-delay. In general, an uncontrolled time-delay in the feedback changes the state of oscillations in an uncertain manner. Therefore, a bounded saturation type feedback with controllable time-delay is proposed for inducing self-excited oscillations. The feedback signal is essentially an infinite weighted sum of a nonlinear function of the state variables of the system measured at equal intervals in the past. More recent is the measurement, higher is the weight. Thus, the feedback signal uses a large amount of information about the past history of the dynamics. Such a control signal can be realized in practice by a recursive means. The control law allows three parameters to be varied namely, the time-delay, feedback and recursive gains. Multiple time scale analysis is used to plot amplitude vs. time-delay curves. Time-delay can be controlled to vary the amplitude of oscillation as well as to switch the oscillation from one mode to the other in a two degrees-of-freedom system. It is shown that a higher recursive gain can exercise a better and a more robust control on the amplitude of oscillation of the system. Analytical results are compared with the results of numerical simulations.     

On the limiting of vibration amplitudes by a sequential friction-spring element

The possibility of using an additional sequentially connected friction spring element in order to reduce vibration amplitudes both for the self-excited oscillations and for the forced vibrations is discussed in the paper. The analysis is based on the averaging technique for systems with “slave variables” and demonstrates two main effects: damping during slipping in the additional element and fast switching between different natural frequencies due to alternating sticking/slipping phases. Analytic predictions for the oscillations’ amplitudes are obtained as steady state solutions of the equations governing slow motions of the system. The obtained analytic results enable optimal choice of friction in order to achieve maximal damping effect in case of the forced vibrations. The reasonable choice of the friction by the self-excited vibrations is a compromise between the acceptable amplitude and the robustness of the corresponding limit cycle. The asymptotic results are confirmed by numeric simulations.     

Generation of pure electrical quadrature amplitude modulation with photonic vector modulator

A photonic vector modulator architecture for generating pure quadrature amplitude modulation (QAM) signals is presented. An electrical quadrature-modulated signal at microwave-millimeter-wave frequencies is generated from its corresponding baseband in-phase (I) and quadrature (Q) components. In the proposed scheme, no electrical devices apart from the electrical tone oscillator are needed in the generation process. In addition, the purity of the generated signal is increased, and the hardware requirements are reduced when compared with previously proposed architectures so a highly compact low-cost architecture can be implemented. A pure 1.25 Gbit/s 4-QAM signal has been experimentally generated at a 42 GHz carrier frequency.     

Determination of the composition and content of pulsed cluster beams from time-of-flight mass spectra of cluster fragments

The properties of a superconducting flux quantum bit (qubit) in the quasidispersive mode, where the frequency of a probe signal is lower than the qubit excitation frequency but is close to it, have been experimentally studied. It has been shown that all parameters of the qubit inductively coupled to a coplanar resonator can be determined at the single-frequency excitation from the analysis of the frequency responses of the transmission of the probe signal at the output of this resonator. Under the additional excitation of the qubit by the signal at the second harmonic of the cavity, resonance dips have been observed because of resonance between the probe signal and induced Rabi splitting. It has been shown that the positions of these dips are in good agreement with the parameters of the qubit that are obtained by analyzing the amplitude–frequency response within the width of the fundamental resonance frequency.     

半导体光放大器非线性失真特性实验研究

对半导体光放大器（SOA）用于1 310 nm残留边带幅度调制（AM-VSB）视频光信号放大时的非线性失真特性进行了实验研究.分析了非线性失真机理.给出了当输入光信号波长位于SOA增益谱下降沿且输入光信号功率较大时,SOA所引入的非线性失真主要由其增益随输入光信号功率变化而波动所造成的结论和对应表达式.提出了减小非线性失真的方法.设计了适合于AM-VSB视频光信号放大的SOA并用于有线电视（CATV）系统实验.研究结果表明,在300 mA的工作电流下,SOA在载频647.25 MHz处引入的组合二阶互调失真（CSO）在－42 dB～－38 dB之间,并随输入光信号功率的增加而变大.     

Non-linear axisymmetric vibration of orthotropic thin circular plates on elastic foundations

This study deals with the large amplitude axisymmetric free vibrations of cylindrically orthotropic thin circular plates resting on elastic foundations. Geometric non-linearity due to moderately large deflections has been included. Movable and immovable simply supported plates and immovable clamped plates resting on Winkler, Pasternak and non-linear Winkler foundations have been considered. The von Kármán type governing equations have been employed. Harmonic vibrations are assumed and the time t is eliminated by the Kantorovich averaging method. An orthogonal point collocation method is used for spatial discretization. Numerical results are presented for the linear natural frequency of the first axisymmetric mode and for the ratio of the non-linear period to the linear period of natural vibration. The effects of foundation parameters, the orthotropic parameter and the edge conditions on the non-linear vibration behaviour have been investigated.     

Sound generation by spheroidal metallic nanoclusters embedded in transparent matrix under the action of laser pulses

The theory of the photo-acoustical effect caused by a laser action on metal nanoclusters embedded in a dielectric matrix is build. The energy absorbed by clusters propagates through the dielectric matrix and generates the sound waves in it via the thermodeformation mechanism. The formulae for an acoustical signal are derived, and the high sensitivity of the sound wave amplitude to the shape of metal clusters, as well to such parameters of a laser irradiation as the frequency, polarization, and intensity, is revealed. The behavior of the sound vibrations amplitude in a region of the surface plasmons absorption is studied in detail. It is found that this amplitude at light absorption by a discrete metal film (a system of clusters in the matrix) can exceed the corresponding amplitude for the absorption by a continuous metal film in the region of plasmon resonances by several orders of magnitude.     

Squeal and chatter phenomena generated in a mountain bike disc brake

This paper examines squeal and chatter phenomena generated experimentally in mountain bike disc brakes. There are two kinds of frictional self-excited vibrations in the bike disc brakes, called squeal with frequency of 1 kHz and chatter with frequency of 500 Hz. In order to reproduce the squeal and chatter, a bench test apparatus using an actual bike was set up to determine the associated frequency characteristics experimentally. The results show the frequencies to be independent of pad temperature and disc rotating speed. Squeal is shown to be in-plane vibration in the direction of the disc surface which is caused by the frictional characteristics having negative slope with respect to the relative velocity in the vibrating system, which includes brake unit, spokes and hub. Chatter is generated within a limited high temperature region. Again, it is frictional vibration in which the squeal and out-of-plane vibration of the disc due to Coulomb friction combine through the internal resonance relation between in-plane and out-of-plane nonlinear vibration caused by the temperature increase of the disc during braking.     

Structural optimization for the avoidance of self-excited vibrations based on analytical models

Self-excited vibrations are a severe problem in many technical applications. In many cases they are caused by friction as for example in disk and drum brakes, clutches, saws and paper calenders. The goal to suppress self-excited vibrations can be reached by active and passive techniques, the latter ones being preferable due to the lower costs. Among design engineers it is known that breaking the symmetries of structures is sometimes helpful to avoid self-excited vibrations. This has been verified from an analytical point of view in a recent paper. The goal of the present paper is to use this analytical insight for a systematic structural optimization of rotors in frictional contact. The first system investigated is a simple discrete model of a rotor in frictional contact. As a continuous example a rotating beam in frictional contact is considered and optimized with respect to its bending stiffness. Finally a brake disk is optimized giving some attention to the feasibility of the modifications for the production process.     

三角波调制对谐振微光学陀螺偏置稳定性的影响

谐振式微光学陀螺是一种新型的惯性传感仪器,与传统的机械陀螺与其他光学陀螺相比具有很多理论上的优势。通过分析抑制载波和提高信噪比,深入地研究了三角波调制频率和幅度对谐振式微光学陀螺偏置稳定性的影响。通过理论计算和仿真分析,考虑得到更好的载波抑制效果,调制幅度应选为15.44 V;考虑提高信噪比,调制频率应设为1 MHz。搭建了谐振式微光学陀螺系统,实验测试结果与理论分析吻合较好。此外,采用优化的调制参数,陀螺的偏置稳定性由0.39 ()/s提高到0.18 ()/s(10 s积分时间)。研究结果表明：选择优化的调制三角波参数可以将陀螺偏置稳定性提高一倍,对于其他调制方案,如正弦波相位调制方案,同样可以通过分析载波抑制和信噪比优化调制参数,改善陀螺偏置稳定性。     

Enhanced switching law for synchronized switch damping on inductor with bimodal excitation

Piezoelectric shunt damping is an emerging field of research. In recent years, a multitude of different electrical circuits have been developed aiming to increase the damping performance and robustness. Synchronized switch damping on inductor (SSDI) is a semi-active control technique that utilizes a passive inductance to build-up a voltage on the piezoceramics that is synchronized with the mechanical vibration. For a single mode excitation the voltage inversion should occur at the moments of maximum deformation, but for multimodal vibrations such a switching law may not be optimal.In this paper a novel switching law for bimodal vibrations is presented using a modal observer. An enhanced voltage build-up is generated by utilizing the vibration energy of the second mode. The amplification of dissipated energy is calculated in an analytical way using normalized parameters, yielding a general result which includes the influence of the frequency and amplitude ratio of the excitation signal. Measurements on a clamped beam test rig are conducted in order to validate the proposed method. An increase of nearly 350 percent in energy dissipation compared to the classical SSDI has been achieved. Furthermore, the increase in energy dissipation is higher than for a previously suggested, comparable switching law.     

三角波调制对谐振微光学陀螺偏置稳定性的影响

谐振式微光学陀螺是一种新型的惯性传感仪器,与传统的机械陀螺与其他光学陀螺相比具有很多理论上的优势。通过分析抑制载波和提高信噪比,深入地研究了三角波调制频率和幅度对谐振式微光学陀螺偏置稳定性的影响。通过理论计算和仿真分析,考虑得到更好的载波抑制效果,调制幅度应选为15.44 V;考虑提高信噪比,调制频率应设为1 MHz。搭建了谐振式微光学陀螺系统,实验测试结果与理论分析吻合较好。此外,采用优化的调制参数,陀螺的偏置稳定性由0.39 ()/s提高到0.18 ()/s(10 s积分时间)。研究结果表明:选择优化的调制三角波参数可以将陀螺偏置稳定性提高一倍,对于其他调制方案,如正弦波相位调制方案,同样可以通过分析载波抑制和信噪比优化调制参数,改善陀螺偏置稳定性。     

小波分析方法在合肥光源逐束团测量系统中的应用

介绍了小波分析方法在逐束团束流位置测量系统中的应用。小波分析方法在高频处频率窗口较宽,具有较高的时间分辨力,使用小波分析可分离并提取信号的振荡成分及基线漂移成分,各成分在时间轴上的位置与原信号相同,原有的线性关系保持不变,在处理非平稳信号时不会造成信号明显劣化,如幅度失真和相位偏差。基于小波分解和重构的时间序列多分辨力滤波处理非平稳信号时不会造成信号明显劣化,保证了追踪束团振荡强度、相位、频率和振荡模式随时间变化的结果更真实可信。在合肥光源中,小波分析方法成功用于横向振荡振幅包络的提取及增长率、阻尼率的计算,也可用于提取横向振荡振幅包络及计算增长率和阻尼率,为机器研究、束流诊断和逐束团反馈系统调试提供了准确的依据。     

小波分析方法在合肥光源逐束团测量系统中的应用

介绍了小波分析方法在逐束团束流位置测量系统中的应用。小波分析方法在高频处频率窗口较宽,具有较高的时间分辨力,使用小波分析可分离并提取信号的振荡成分及基线漂移成分,各成分在时间轴上的位置与原信号相同,原有的线性关系保持不变,在处理非平稳信号时不会造成信号明显劣化,如幅度失真和相位偏差。基于小波分解和重构的时间序列多分辨力滤波处理非平稳信号时不会造成信号明显劣化,保证了追踪束团振荡强度、相位、频率和振荡模式随时间变化的结果更真实可信。在合肥光源中,小波分析方法成功用于横向振荡振幅包络的提取及增长率、阻尼率的计算,也可用于提取横向振荡振幅包络及计算增长率和阻尼率,为机器研究、束流诊断和逐束团反馈系统调试提供了准确的依据。     

On Complex Delay Time of a Narrow-Band Signal Passing through a Resonant Filter

It is shown that distortion of a narrow-band signal with a gradually varying envelope during passage through a resonant filter can approximately be described in terms of complex delay time. The real part of the delay time can be both positive and negative, depending on the filter type and the carrier frequency of the signal. The imaginary part of the delay time leads to a distortion of the complex envelope of the signal. The intensity envelope of signals without frequency modulation is distorted only slightly, while distortion is considerable even in the case of a fairly small frequency modulation. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 8, pp. 711–718, August 2005.     

Effect of a constant magnetic field on echo signals in high-temperature superconductor powders

The generation of acoustic and vortex oscillations in high-temperature superconductor (HTSC) powders excited by radiofrequency (rf) pulses was analyzed in detail in our earlier publications. The rf magnetic field stimulates oscillations of magnetic vortices on the surface of an HTSC grain, which are transformed into lattice vibrations via the pinning centers at the surface, thus inducing a propagating acoustic wave. The allowance for second-order nonlinearity in the gradient of deviation of the crystal lattice from its equilibrium position in the equation for the acoustic wave leads to a dependence of the natural frequency of crystal lattice vibrations on the amplitude and duration of pulses exciting these vibrations. Such a dependence is responsible for echo signals that can be detected experimentally. The proposed model makes it possible to interpret most experimental results for BiPbSrCaCuO superconducting samples. We consider the effect of a constant magnetic field on the amplitude and the echo signal decay time. We observed a clearly manifested peak that was not described by other authors. The model proposed here provides an obvious explanation for this peak.     

Quenching of self-excited vibrations: one- and two-frequency vibrations

An analysis is presented of the possibility of initiation of two-frequency self-excited vibrations, and it is shown on this basis, and amply documented by analogue solutions, that the occurrence of such a phenomenon is rather exceptional in the systems being examined. It also is shown that unless the value of the coefficient of additional damping is very close to that lying on the boundary of the stability of the equilibrium position, it will have little effect on reducing the amplitude of self-excited vibrations even in the case of optimum tuning.     

Visualization of nonuniform magnetic fields by garnet ferrite films

The magnetization distribution in epitaxial garnet ferrite films subjected to the harmonic field of a signal from a magnetic tape is studied. By means of image processing techniques and diffraction spectrum analysis, it is shown that the distortion of the signal shape grows with increasing amplitude and period of the field.     

Generalised modal stability of inclined cables subjected to support excitations

Parametric excitation is of concern for cables such as on cable-stayed bridges, whereby small amplitude end motion can lead to large, potentially damaging, cable vibrations. Previous identification of the stability boundaries for the onset of such vibrations has considered only a single mode of the cable, ignoring non-linear coupling between modes, or has been limited to special cases. Here multiple cable modes in both planes are included, with support excitation close to any natural frequency. Cable inclination, sag, parametric and direct excitation and nonlinearities, including modal coupling, are included. The only significant limitation is that the sag is small. The method of scaling and averaging is used to find the steady-state amplitude of the directly excited mode and, in the presence of this response, to define stability boundaries of other modes excited parametrically or through nonlinear modal coupling. It is found that the directly excited response significantly modifies the stability boundaries compared to previous simplified solutions. The analysis is validated by a series of experimental tests, which also identified another nonlinear mechanism which caused significant cable vibrations at twice the excitation frequency in certain conditions. This new mechanism is explained through a refinement of the analysis.     

Lock-in and quasiperiodicity in hydrodynamically self-excited flames: Experiments and modelling

Hydrodynamically self-excited flames are often assumed to be insensitive to low-amplitude external forcing. To test this assumption, we apply acoustic forcing to a range of jet diffusion flames. These flames have regions of absolute instability at their base and this causes them to oscillate at discrete natural frequencies. We apply the forcing around these frequencies, at varying amplitudes, and measure the response leading up to lock-in. We then model the system as a forced van der Pol oscillator.Our results show that, contrary to some expectations, a hydrodynamically self-excited flame oscillating at one frequency is sensitive to forcing at other frequencies. When forced at low amplitudes, it responds at both frequencies as well as at several nearby frequencies, indicating quasiperiodicity. When forced at high amplitudes, it locks into the forcing. The critical forcing amplitude for lock-in increases both with the strength of the self-excited instability and with the deviation of the forcing frequency from the natural frequency. Qualitatively, these features are accurately predicted by the forced van der Pol oscillator. There are, nevertheless, two features that are not predicted, both concerning the asymmetries of lock-in. When forced below its natural frequency, the flame is more resistant to lock-in, and its oscillations at lock-in are stronger than those of the unforced flame. When forced above its natural frequency, the flame is less resistant to lock-in, and its oscillations at lock-in are weaker than those of the unforced flame. This last finding suggests that, for thermoacoustic systems, lock-in may not be as detrimental as it is thought to be.