Fractal-geometry simulation of a lightning discharge

It is suggested that a wideband lightning discharge be approximated by a damped periodic oscillation. With such an approach, the oscillation frequency and relaxation time are introduced and it is found that lightning radiates over a distance of several tens of kilometers. This length is much greater than the lightning bolt’s apparent length (several kilometers). The difference between the lengths is explained using fractal geometry. In terms of fractal geometry, the lightning discharge is so tortuous that an actually very long lightning bolt is accommodated by a short straight line. An attempt is made to determine the fractal dimension of tortuous and intermittent lightning bolts.     

A parametrically driven harmonic analysis of a non-linear stretched string with time-varying length

This paper is concerned with the first, second and third harmonic lateral vibrations of a string having a forced, periodic, small length variation. Account is taken of the non-linear term arising from the correction to the tension of the string due to local elongation. It is found that increasing the amplitude of the length variation of the string results in a narrowing of the frequency response range of each of the harmonic oscillation components. Both numerical and analytical calculations of the harmonic frequency responses have been carried out The relationships for initial values between the original differential equation and the approximate differential equations for the harmonic responses are discussed in detail.     

无内共振时的扬声器分谐波

研究了驱动频率低于扬声器辐射体薄壳轴对称模态最低固有频率的扬声器1/2分谐波失真。采用以位敏探测器作为光电传感器的激光三角法实验观测扬声器振膜的振动位移和模态,确定了参与的非轴对称模态的周向波数。采用多尺度法求解了扬声器的非线性模态方程。给出了扬声器分谐波的阈值电压公式。结果表明扬声器辐射体薄壳的分谐波失真源于直接激励的轴对称模态耦合激发了非轴对称模态的振动,这种耦合激励表现为参数激励。增大扬声器振膜材料的损耗因子、杨氏模量和厚度可提高产生分谐波的阈值电压。      

Theory of the Magnetomechanical pole effect

The vibration frequencies of a magnetized reed can be affected by a magnetic field due to the periodic change in the interaction energy between the field and the reed. This effect was first studied by Berry and Pritchet who called it the pole effect according to a simplifying assumption made in evaluating this interaction energy. We gave here an exact first-order theory for the case of clamped-free and free-free flexural vibrations. We also give experimental evidence and the corresponding theory for a similar effect occurring with torsional vibrations.     

Time-domain simulation of sound production of the sho

A physical model based on the sound production mechanism of the sho is proposed with intention of applying it to sound synthesis. Time-domain simulation was done using this model, and effects of the tube length and blowing pressure on the sounding frequency and sounds spectra were investigated. The reed vibration, pressure variation inside the tube, and threshold blowing pressure for oscillation were measured by artificially blowing air into the sho. The experimental results are in acceptable agreement with simulation results in terms of the relationships between tube length and threshold pressure and between tube length and the sounding frequency. In addition, recorded sound waveforms and simulated ones have a common feature in the sense that high-frequency components of their spectra increase with increasing blowing pressure. Further, it is concluded that a sho reed acts as an "outward-striking valve."     

A numerical model for the 3-D non-linear vibrations of an N-string

We present a non-linear numerical model describing the 3-D vibrations of a planar network of N sections of string which are connected together at one common mobile extremity. We call such a network N-string. For small-amplitude vibrations perpendicular to the N-string equilibrium plane, the numerical results coincide with the already known analytical solutions of the linear model. This non-linear model makes it possible to describe small- or large-amplitude 3-D vibrations of any kind of N-string subjected to an initial plucking. The equations of motion are also presented in a dimensionless form and a vast dimensionless physical parameter space is identified. The numerical model can be extended to more complex networks of strings.     

Oscillation threshold of a clarinet model: a numerical continuation approach

This paper focuses on the oscillation threshold of single reed instruments. Several characteristics such as blowing pressure at threshold, regime selection, and playing frequency are known to change radically when taking into account the reed dynamics and the flow induced by the reed motion. Previous works have shown interesting tendencies, using analytical expressions with simplified models. In the present study, a more elaborated physical model is considered. The influence of several parameters, depending on the reed properties, the design of the instrument or the control operated by the player, are studied. Previous results on the influence of the reed resonance frequency are confirmed. New results concerning the simultaneous influence of two model parameters on oscillation threshold, regime selection and playing frequency are presented and discussed. The authors use a numerical continuation approach. Numerical continuation consists in following a given solution of a set of equations when a parameter varies. Considering the instrument as a dynamical system, the oscillation threshold problem is formulated as a path following of Hopf bifurcations, generalizing the usual approach of the characteristic equation, as used in previous works. The proposed numerical approach proves to be useful for the study of musical instruments. It is complementary to analytical analysis and direct time-domain or frequency-domain simulations since it allows to derive information that is hardly reachable through simulation, without the approximations needed for analytical approach.     

Nonlinear vibrations of clamped-free circular cylindrical shells

Only experimental studies are available on large-amplitude vibrations of clamped-free shells. In the present study, large-amplitude nonlinear vibrations of clamped-free circular cylindrical shell are numerically investigated for the first time. Shells with perfect and imperfect shape are studied. The Sanders-Koiter nonlinear shell theory is used to calculate the elastic strain energy. Shell displacement fields (longitudinal, circumferential and radial) are expanded by means of a double mixed series, i.e. harmonic functions for the circumferential variable and Chebyshev polynomials for the longitudinal variable. All boundary conditions are satisfied. The system is discretized by using natural modes of the shell and Lagrange equations by an energy approach, retaining damping through Rayleigh's dissipation function. Different expansions involving from 18 to 52 generalized coordinates are used to study the convergence of the solution. The nonlinear equations of motion are numerically studied by using arclength continuation method and bifurcation analysis. Numerical responses to harmonic radial excitation in the spectral neighborhood of the lowest natural frequency are compared with experimental results available in literature. The effect of geometric imperfections and excitation amplitude are numerically investigated and fully explained.     

Self-excited subharmonic oscillations in plasmas produced by local electron cyclotron resonance

A self-excitation of subharmonics and their higher harmonics of a low frequency oscillation which seems to be ascribed to the current-convective instability is observed.     

Suppression of the primary resonance vibrations of a forced nonlinear system using a dynamic vibration absorber

In a single degree-of-freedom weakly nonlinear oscillator subjected to periodic external excitation, a small-amplitude excitation may produce a relatively large-amplitude response under primary resonance conditions. Jump and hysteresis phenomena that result from saddle-node bifurcations may occur in the steady-state response of the forced nonlinear oscillator. A simple mass-spring-damper vibration absorber is thus employed to suppress the nonlinear vibrations of the forced nonlinear oscillator for the primary resonance conditions. The values of the spring stiffness and mass of the vibration absorber are significantly lower than their counterpart of the forced nonlinear oscillator. Vibrational energy of the forced nonlinear oscillator is transferred to the attached light mass through linked spring and damper. As a result, the nonlinear vibrations of the forced oscillator are greatly reduced and the vibrations of the absorber are significant. The method of multiple scales is used to obtain the averaged equations that determine the amplitude and phases of the first-order approximate solutions to primary resonance vibrations of the forced nonlinear oscillator. Illustrative examples are given to show the effectiveness of the dynamic vibration absorber for suppressing primary resonance vibrations. The effects of the linked spring and damper and the attached mass on the reduction of nonlinear vibrations are studied with the help of frequency response curves, the attenuation ratio of response amplitude and the desensitisation ratio of the critical amplitude of excitation.     

Some aspects of the harmonic balance method applied to the clarinet

The clarinet has been extensively studied by various theoretical and experimental techniques. In this paper, the harmonic balance method (HBM), a numerical method mainly working in the frequency domain, has been applied to solve a simple nonlinear clarinet model consisting of a linear exciter (for the reed) nonlinearly coupled to a linear resonator with visco-thermal losses (for the pipe). A recent and improved implementation of the HBM for self-sustained instruments has allowed us to study the model theoretically when including dispersion in the pipe or mass and damping terms in the reed model. The resulting periodic solutions for the internal pressure spectrum and the corresponding playing frequency are shown to align well with previous theoretical and experimental knowledge of the clarinet. Finally, we present and briefly discuss a few (probably unstable) oscillation regimes both with the HBM and with a real clarinet.     

一类非自治位置时滞反馈控制系统的亚谐共振响应

研究了弹性轨道条件下，控制回路中位置反馈信号存在时滞的磁浮系统在亚谐轨道激励作用下的响应问题. 将动力学模型在平衡点处线性化，以时滞为分岔参数，得到了系统出现Hopf分岔的条件. 用中心流形约化方法得到了包含轨道扰动系统的Poincaré规范型. 用多尺度法从理论上推导了时滞磁浮系统的亚谐共振周期解，得到了自由振动的分岔响应方程，分析了周期解中自由振动项的存在条件，研究了控制参数和激励参数与周期解的关系. 最后用数值仿真的方法分析了时滞参数、控制参数对系统响应的影响，分析结果指出，使系统保持稳定的亚谐响应的时滞边界小于无扰动时的时滞边界，时滞参数不但可以抑制亚谐响应，还能够控制混沌的产生，而控制参数可以控制系统响应中自由振动项的出现和受迫振动的幅值，适当选择这些参数可以有效抑制亚谐振动响应. 关键词： 亚谐共振响应 位置时滞反馈控制 非自治磁浮系统 分岔     

口琴簧片振动频率的理论与实验研究

口琴是常见的乐器之一。通过推导了口琴簧片振动频率的计算公式,进而揭示了簧片几何尺寸对振动频率的影响,并对录制好的口琴音频文件进行快速傅里叶变换（FFT）,从而推断口琴簧片振动的频率。     

Noncontact modal analysis of a pipe organ reed using airborne ultrasound stimulated vibrometry

The goal of this study was to excite and measure, in a noncontact manner, the vibrational modes of the reed from a reed organ pipe. To perform ultrasound stimulated excitation, the audio-range difference frequency between a pair of ultrasound beams produced a radiation force that induced vibrations. The resulting vibrational deflection shapes were measured with a scanning laser vibrometer. The resonances of any relatively small object can be studied in air using this technique. For a 36 mm x 6 mm brass reed, displacements and velocities in excess of 5 microm and 4 mm/s could be imparted at the fundamental frequency of 145 Hz. Using the same ultrasound transducer, excitation across the entire range of audio frequencies was obtained. Since the beam was focused on the reed, ultrasound stimulated excitation eliminated background effects observed during mechanical shaker excitation, such as vibrations of clamps and supports. The results obtained using single, dual and confocal ultrasound transducers in AM and two-beam modes, along with results obtained using a mechanical shaker and audio excitation using a speaker are discussed.     

Generation of phase nuclei by solitons of the new “undulator” type in martensitic phase transitions of crystalline materials

The microdynamics of large-amplitude nonlinear lattice vibrations of plutonium and uranium materials has been investigated at high reactor temperatures in the ranges of martensitic phase transitions. Topologically new large-amplitude solitons of the “undulator” type have been revealed. Transverse and longitudinal “undulator” solitons in crystals with hexagonal and cubic symmetry, depending on the direction of motion, have different kinematic and amplitude characteristics, which differ from the characteristics of the previously known solitons. The transverse “undulator” solitons, like electrons in undulators, are observed with periodic atomic displacements orthogonal to the direction of soliton propagation. The longitudinal “undulator” solitons with displacements of atoms in the direction of soliton propagation are characterized by periodic delays with two-step velocities on the trajectory in a certain analogy with two-period engineering undulator devices. It has been shown that, at high energies, such “undulator” solitons of two types generate nuclei of a new phase in early stages of structural phase transitions.     

Influence of the periodic motion of a monochromatic light source on the spectrum of its radiation

The influence of the periodic motion of a monochromatic light source on the observed spectrum of its radiation in the far-field and near-field zones is considered. The appearance of components shifted in frequency (harmonics of the oscillation frequency of the source) is demonstrated. The spatial structure of harmonics is investigated, and the presence of optical vortices in these harmonics is shown.     

Acoustic characteristics of rough voice: Subharmonics

This study investigates the relationship between rough voice and the presence of Subharmonics, which correspond to smaller yet distinct peaks located between two consecutive harmonic peaks in the power spectrum. Spectrum analysis was undertaken in 389 pathologic voices, of which 20 had subharmonics. Although all 20 voices had roughness perceptually, 8 had normal jitter and/or shimmer. The degree of roughness had a significant inverse relationship with the frequency of subharmonics. By digital signal processing, sound samples with various types of subharmonics were synthesized and perceptually analyzed. Power and frequency of subharmonics in the synthesized sound also had significant relationships with the degree of roughness. Rough voice is acoustically characterized not only by jitter and shimmer but also by the presence of subharmonics in the power spectrum. Subharmonics are important acoustic properties for objective evaluation of rough voices.     

Response of a PCF-based modal interferometer to lateral stress: Resonant behavior and performance as sensor

The performance of a fiber-based modal interferometer as lateral stress sensor has been analyzed, both for static and periodic forces applied on it. The central fiber of the interferometer is a photonic crystal fiber. Forces are applied on it perpendicular to its axis, so that they squeeze it. In static situations, changes in the transmission spectrum of the interferometer are studied as a function of the charges applied. Measurements with several interferometers have been carried out in order to analyze the influence of its length and of its splices’ transmission on the device operation, looking for optimization of its linearity and sensibility. The effect of periodic charges, as an emulation of vibrations, has also been studied. The analysis is centered on the frequency dependence of the response. In linear regime (small enough periodic charges), the results obtained are satisfactorily explained by treating the central fiber of the interferometer as a mechanical resonator whose vibration modes coincide with the ones of a cylinder with clamped ends. In nonlinear regime, period doubling and other anharmonic behaviors have been observed.