An analysis of the distortion effects of Coulomb damping on the vector plots of lightly damped systems

An analysis of the vector plot responses of lightly damped single degree-of-freedom systems with Coulomb damping has been made. The vector plots, as derived by using both an exact and an approximate method (the method of harmonic balance) are compared and it is shown that the distortion of the normally circular vector locus is due to the Coulomb damping. Although the vector plots of such systems are distorted it is also shown that the frequency gradient criterion is still applicable for location of a natural frequency even when the frictional force levels approach the excitation force levels. To permit estimation of the modal damping of these systems a criterion by means of which the limits of the useful frequency range can be specified is suggested. The criterion, which is based upon the quadrature input power necessary to excite the mode of vibration, is found to be equivalent to that obtained from the half power point theory when applied to linear systems.     

光梯度力驱动纳谐振器的非线性动力学特性研究

光梯度力作为纳谐振器的一种新型驱动方式,得到了广泛关注.本文研究了光梯度力的固有非线性特性,建立了光梯度力驱动圆环与辐条谐振系统的动力学模型.揭示了入射光功率以及几何参数对系统的非线性动力学响应的影响规律.研究表明:光梯度力会引起系统呈现刚度软化效应,随着入射光功率增大,系统主共振峰值明显增大,且谐振频率随着振幅增大而产生较大偏移;两环初始间隙增大,系统振动幅值和谐振频率均下降;辐条厚度越大,系统主共振峰值和谐振频率均减小.因此,可以通过调节入射光功率来实现圆环辐条谐振器的频率调节,为光梯度力驱动纳谐振器动力学设计和性能预测提供理论参考.     

Objectively measured and subjectively perceived distortion in nonlinear systems

A method for measuring nonlinear distortion, which is applicable to almost any transmission system and which can use any input signal as a test signal, is proposed. The method exploits the fact that a pair of signals, generated to form the real and imaginary parts of the analytical signal corresponding to the input signal to a system, lose their property of being a Hilbert pair after being passed through a nonlinear system. The method was tested by measuring 12 different hearing aid compression systems. These objective measurements were compared with the subjectively perceived amount of distortion, assessed by a group of 10 otologically normal subjects. A reasonably monotonic relation between the subjective and objective measures of distortion was observed. The objective Hilbert pair based measure can be related to both traditional total harmonic distortion and traditional signal to noise ratio.     

Nonlinear Resonance Cone Surfaces

The nonlinear modification of the equation describing the surface (the resonance cone) on which the maximum electric field occurs in a magnetized plasma excited by an arbitrary, axially symmetric, localized RF source is derived. The nonlinearity is assumed to be due to the ponderomotive force. The nonlinear modification of the slope of the resonance cone is most pronounced near the plasma and upper hybrid frequencies, and is inversely proportional to the distance from the exciter. For frequencies of the lower branch the slope is decreased, whereas for upper branch frequencies the slope is increased.     

Instability analysis in oscillators with velocity-modulated time-varying stiffness—Applications to gears submitted to engine speed fluctuations

A one degree-of-freedom model is set up which incorporates time-varying mesh stiffness functions and the influence of unsteady input rotations due to engine speed fluctuations. The stability of the associated parametrically excited system is analysed by calculating the monodromy matrix via a Newmark scheme. A piecewise constant and a sinusoidal mesh stiffness functions are considered and it is shown that additional side-band instability zones are generated because of frequency modulations. The influence of the mesh stiffness variations and damping is discussed.     

突变截面驻波管和极高纯净驻波场的实验研究

突变截面驻波管属于失谐驻波管,即其高阶共振频率不是一阶共振频率的整数倍。通过对STAS的优化设计,利用STAS的失谐性质在一阶和二阶共振频率下激励分别获得了180 dB和177 dB的极高纯净驻波声场。尽管声压级已经很高,但在接下来的对一阶和二阶共振频率激励下的声波波形畸变和谐波饱和情况进行的实验研究中仍然没有观察到谐波饱和现象。与此同时,对三阶共振频率激励下的声场进行了实验研究,由于三阶共振频率激励下的大振幅非线性声场的二次谐波频率接近六阶共振频率,在声压级达到170 dB时观测到了三阶共振频率激励下的声波波形畸变和谐波饱和现象。      

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.     

Nonlinear vibration of micromachined asymmetric resonators

In this paper, the nonlinear dynamics of a beam-type resonant structure due to stretching of the beam is addressed. The resonant beam is excited by attached electrostatic comb-drive actuators. This structure is modeled as a thin beam-lumped mass system, in which an initial axial force is exerted to the beam. This axial force may have different origins, e.g., residual stress due to micro-machining. The governing equations of motion are derived using the mode summation method, generalized orthogonality condition, and multiple scales method for both free and forced vibrations. The effects of the initial axial force, modal damping of the beam, the location, mass, and rotary inertia of the lumped mass on the free and forced vibration of the resonator are investigated. For the case of the forced vibration, the primary resonance of the first mode is investigated. It has been shown that there are certain combinations of the model parameters depicting a remarkable dynamic behavior, in which the second to first resonance frequencies ratio is close to three. These particular cases result in the internal resonance between the first and second modes. This phenomenon is investigated in detail.     

具有频率涨落的简谐力激励下线性谐振子的随机共振

针对线性谐振子受到具有频率涨落的简谐力激励的情况, 计算出系统响应的一阶矩解析表达式.研究发现系统的输出响应以固有频率振动, 响应振幅随简谐激励力频率的变化出现"真实"随机共振,随固有频率的变化出现抑制和 共振两种现象.     

Comments on the picosecond pulse width measurement by the single-shot second harmonic beam technique

We show that the measurement of the ultrashort light pulse duration by the single-shot second harmonic beam technique requires caution. It is found that the far-field distribution of the second harmonic radiation from non bandwidth-limited pulses shows a pronounced structure even if the near-field pattern is without structure. This interference effect is interpreted as being due to the special symmetry properties of the spatial coherence of the second harmonic beam. A simple method for a quick determination of the existence of the bandwidth-limited relation in an individual picosecond light pulse is proposed.     

Harmonic generation by an interaction of laser with an array of anharmonic carbon nanotubes

A scheme of second and third harmonic generation from laser irradiated anharmonic carbon nanotubes (CNTs) embedded in silica is proposed. An intense ultra short laser pulse interacting with the array of CNTs displaces its electrons. When this displacement becomes comparable to the radius of electrons of CNTs, the restoring force of electrons varies nonlinearly with the displacement. As a result, plasmon resonance gets broadened and the large resonance absorption of the laser by the electrons of CNTs occurs. The power conversion efficiency of harmonic generation due to the anharmonicity of CNTs is much higher than that due to the ponderomotive force nonlinearity. The effect of amplitude modulated parameter on the amplitude of second and third harmonic is studied. The high amplitude of generated harmonics can be realized with the amplitude modulated laser as compared to ordinary unmodulated laser.     

Correcting Low-Frequency Phase Distortion in Electroglottograph Waveforms

Dynamic high-pass filtering with a -3 dB frequency that is a factor of ten or more below the voice fundamental frequency has a negligible effect on the amplitudes of the Fourier components of an EGG waveform. However, such a filter can significantly distort the waveform due to distortion in the phase or time alignment of these Fourier components. Such high-pass filtering can be introduced purposefully to stabilize the waveform by attenuating low-frequency noise, or may be an undesired effect of using an amplification or data acquisition system designed for acoustic signals. For a given voice fundamental frequency, the amount of distortion depends greatly on the order or attenuation characteristics of the filter and on the type of EGG waveform. Both a high-order filter and a breathy voice tend to increase the amount of distortion. If the characteristics of the high-pass filter are known, there are a number of digital filter techniques that can be used to reduce the phase distortion. However, it is shown that a relatively simple analogue network can also be used to obtain a correction that suffices for most applications. If the precise characteristics of the filter are not known, the response to a square wave can be used to adjust the compensator parameters for an optimal correction.     

扬声器辐射体旋转薄壳的谐波失真

研究了扬声器辐射体旋转薄壳几何非线性引起的谐波失真。采用摄动法和有限元法确定了2次和3次谐波振型,计算了薄壳材料参数和几何参数对谐波失真的影响。结果表明扬声器薄壳谐波失真的机制是分割振动模态的基波共振和超谐波共振,以基波共振为主。采用高阻尼、大杨氏模量和低密度的振膜材料可以降低振膜谐波失真;厚度对谐波失真的峰值影响不大;锥壳半顶角过大,可使3次谐波明显增大。      

Fine Structure of the Local Alfven Resonances in Cold Plasma Placed in Bumpy Magnetic Field

Unlike in the case of an axial magnetic field, in which each mode of electromagnetic wave excited by an external source propagates independently, ripples in a bumpy magnetic field cause the wave to propagate as a wave envelope that contains also satellite harmonics in addition to the main harmonic. The influence of this multimodity on the distribution of electromagnetic waves within the local Alfven resonance regions is studied and compared for the following three cases. In the first case, Alfven resonance takes place for a main harmonic of the wave. In the second case, Alfven resonance occurs in the same region for two main harmonics which are coupled due to the plasma periodic axial inhomogeneity. Alfven resonance for a satellite harmonic is considered in the third case.     

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.     

An Experimental Investigation of Second Harmonic Generation in a Cyclotron and Upper Hybrid Resonant Plasma

An experiment is described in which an electromagnetic wave (extraordinary mode) is propagated across a magnetized plasma and second harmonic generation is detected. The generation of the plasma and the second harmonic wave is associated with resonant conditions of electron cyclotron resonance and upper hybrid resonance. By adjusting the intensity of axial magnetic field, the second harmonic generation can be made solely due to the electron cyclotron resonance, the upper hybrid resonance or both. The experiment is qualitatively in agreement with previous similar experiments and can be explained in terms of the spatial variations of the magnetic field intensity and the electron number density. A technique for diagnosing peak number density is developed from the observed second harmonic power characteristics.     

Distribution of the probability of oscillations of the surface of liquid hydrogen in the turbulent regime

The probability distribution density of the deviation of the surface of liquid hydrogen from the equilibrium plane state in the system of capillary waves has been analyzed. It has been shown that this probability distribution density for the case of the excitation of the surface oscillations by low-frequency noise in the turbulent regime is well reproduced by a Gaussian. When the oscillations are excited by a low-frequency harmonic force, the stochastization of the waves occurs after several scattering events.     

The anharmonic force field of phosphorus trifluoride from the millimeter wave spectra of vibrationally excited states

The millimeter rotational spectra of PF₃ have been recorded for all four excited fundamental vibrational states. A coriolis resonance between ν₁ and ν₃ results in anomalous distortion constants for these states and can be analyzed to yield $\text{|ζ}{}_{13}{}^{\mathrm{y}}\text{| = 0.392}$. The value of $\text{ζ}{}_{33}{}^{\mathrm{c}}$ is found to be 0.4194 which does not fit the coriolis sum rule due to anharmonic resonance. Equilibrium values for the centrifugal distortion constants are determined and have been used to find the harmonic force field. All available data is used to determine some of the anharmonic force constants.     

Mechanisms for second harmonic generation in the interaction of a superintense ultrashort laser pulse with cluster plasma

The effects of the interaction of an intense femtosecond laser pulse with large atomic clusters are considered. The pulse intensity is of the order of 10¹⁸ W cm^?2. New effects appear when the magnetic component of the Lorentz force is taken into account. The second harmonic of laser radiation is generated. The second harmonic generation (SHG) efficiency is proportional to the square of the number of atoms in a cluster and the square of the laser radiation intensity. The resonance increase in the SHG efficiency at the Mie frequencies (both at the second harmonic frequency and fundamental frequency) proved to be insignificant because of the fast passage through the resonance during cluster expansion. The mechanisms of the expansion and accumulation of energy by electrons and ions in the cluster are discussed in detail. The energy accumulation by electrons mainly occurs due to stimulated inverse bremsstrahlung upon elastic reflection of the electrons from the cluster surface. The equations describing the cluster expansion take into account both the hydrodynamic pressure of heated electrons and the Coulomb explosion of the ionized cluster caused by outer shell ionization. It is assumed that both inner shell and outer shell ionization is described by the over barrier mechanism. It is shown that atomic clusters are more attractive for the generation of even harmonics than compared to solid and gas targets.     

Subharmonic excitation of the eigenmodes of charged particles in a Penning trap

When parametrically excited, a harmonic system reveals a nonlinear dynamical behaviour which is common to non-deterministic phenomena. The ion motion in a Penning trap -- which can be regarded as a system of harmonic oscillators -- offers the possibility to study anharmonic characteristics when perturbed by an external periodical driving force. In our experiment we excited an electron cloud stored in a Penning trap by applying an additional quadrupole r.f. field to the endcaps. We observed phenomena such as individual and center-of-mass oscillations of an electron cloud and fractional frequencies, so-called subharmonics, to the axial oscillation. The latter show a characteristic threshold behaviour. This phenomenon can be explained with the existence of a damping mechanism affecting the electron cloud; a minimum value of the excitation amplitude is required to overcome the damping. We could theoretically explain the observed phenomenon by numerically calculating the solutions of the damped differential Mathieu equation. This numerical analysis accounts for the fact that for a weak damping of the harmonic system we observed an even-odd-staggering of the the different orders of the subharmonics in the axial excitation spectrum.Received: 22 September 2003, Published online: 2 December 2003PACS: 52.27.Jt Nonneutral plasmas - 82.80.Qx Ion cyclotron resonance mass spectrometry