线性时滞反馈引起的周期性振动共振分析

研究了高频信号和微弱低频信号同时激励下线性时滞反馈对过阻尼双稳系统和Duffing振子系统中振动共振现象的影响. 解析分析和数值结果都表明, 系统对低频信号的响应幅值增益随时滞参数的变化同时呈现两种不同的周期性关系, 其周期分别为输入的高频信号和低频信号的周期. 数值结果还表明, 对不存在经典振动共振现象的单稳Duffing系统, 通过调节时滞参数也可以引发振动共振现象. 使用时滞反馈不仅可以有效地控制振动共振, 还可以进一步增强系统对微弱低频信号的响应. 关键词： 双稳系统 Duffing 系统 线性时滞反馈 振动共振     

分数阶双稳系统中的非周期振动共振

在受二进制非周期信号和周期方波信号激励的分数阶双稳系统中,研究了非周期振动共振问题,用于微弱非周期信号的检测和增强.当非周期信号脉宽较大时,系统为小参数,通过调节周期方波信号的幅值,能够实现非周期振动共振.当非周期信号脉宽较小时,分别通过变尺度法和二次采样法实现了非周期振动共振.使用变尺度法,得到的大参数等价系统能够匹配任意小的非周期信号脉宽,其中变尺度系数是该方法在使用过程中需要选择的关键参数.使用二次采样法,二次采样后得到的非周期信号具有较大的脉宽,能够匹配原先的小参数系统,其中二次采样频率比是该方法使用过程中的关键参数.这两种方法虽然实现非周期振动共振的物理过程不同,但能够达到相同的效果.系统阶数对振动共振产生影响,随着阶数的增大,发生最佳振动共振时所需要的辅助信号幅值变大,同时系统输出的最佳时间序列与输入非周期信号之间的相似性增强.     

纵向驱动弦的次频振动实验分析

讨论纵向驱动弦时的次频驻波振动现象,与弦运动轨迹的观察方法。根据弦运动轨迹,用仿真分析谐波振动可获得弦振动的有关物理信息。实验观察到,可出现非共振驻波(次频振动)振幅可比共振驻波振幅大的多现象。     

压电陶瓷元件在物理演示实验中的应用

压电陶瓷元件是一种电声元件,它既有效果良好的压电效应,也有显著的逆压电效应,即电致伸缩效应。此外,压电陶瓷元件还具有价格低廉、外形轻而薄、功耗低、耐高压等优点。因此,利用实验室常备的慢扫描示波器,低频信号发生器,各种频率的音叉及共鸣箱、扩音机,配上几片压电陶瓷元件就可以演示电学、振动与波等物理内容。常用的压电陶瓷元件的型号、尺寸及简单构造分别列在下表和图1(a)中     

一类五次方振子系统的叉形分叉及振动共振研究

研究了一类具有分数阶导数阻尼的五次方振子系统中的叉形分叉及振动共振现象. 基于快慢变量分离法, 消去系统中的高频激励成分, 得到关于慢变量的等效系统, 根据等效系统中稳态平衡点的变化情况研究了系统的叉形分叉现象. 结果表明: 高频信号幅值的递增变化会引起亚临界叉形分叉, 高频信号频率和分数阶导数阻尼阶数的递增变化都会引起超临界叉形分叉; 振动共振和叉形分叉是关联的, 当叉形分叉发生时, 振动共振曲线会出现两个峰值, 否则只会出现一个峰值. 通过解析结果和数值模拟结果的对比, 验证了解析分析的正确性. 关键词： 亚临界叉形分叉 超临界叉形分叉 分数阶导数阻尼 振动共振     

周期性弦链系统振动模研究实验介绍

围绕物理、技术和能力培养的课程目标,详细地介绍了北京大学近代物理实验课中"周期性弦链系统振动模研究"的建设和教学情况.周期性弦链系统是一段等间距穿有小球的细弦.实验要求用动态信号分析仪获得不同实验条件下的几种有限周期弦链的振动谱,并由此得到对应的无限长弦链的振动谱结构.此实验有助于理解周期性与带状谱结构之间的关系,了解动态信号分析技术,也比较适合于训练在数学抽象与物理图像间建立联系的能力.     

双频信号驱动含分数阶内、外阻尼Duffing振子的振动共振

本文利用解析和数值的方法研究了由双频周期信号驱动含分数阶内、外阻尼的Duffing振子的振动共振现象,并讨论了分数阶阶数对上述现象的影响. 研究发现：双频周期信号同时驱动的分数阶Duffing振子响应幅值增益Q可随着高频周期激励幅值的改变达到最大值,即出现了和整数阶非线性动力系统相似的振动共振现象,而相应的分数阶导数项则分别为系统提供了内、外两种阻尼力从而导致了系统有效势函数的改变,进而引发了比整数阶动力系统更为丰富的振动共振现象. 关键词： 振动共振 Duffing振子 分数阶阻尼 分数阶系统     

基于振动共振的随机共振控制

分析了非线性双稳系统在高、低两种不同频率信号作用下的动力学特性，给出了高频信号参数与双稳系统输出信号的信噪比和功率谱放大率关系的解析表达式，提出了基于振动共振的随机共振控制方法.理论分析和数值仿真结果表明，通过调节高频信号的幅值或频率大小，能有效地控制双稳系统输出信号的信噪比和功率谱放大率.     

利用LabVIEW改进弦振动实验仪

对传统弦振动实验进行改进,利用LabVIEW的图形化程序设计及数据采集卡的LabVIEW函数调用,编写LabVIEW程序控制采集弦振动信号的数据采集卡,实现弦振动信号的计算机显示,并通过编写LabVIEW程序进行傅里叶变换频谱分析.     

双频信号驱动含分数阶内、外阻尼Dufng振子的振动共振

本文利用解析和数值的方法研究了由双频周期信号驱动含分数阶内、外阻尼的Dufng振子的振动共振现象,并讨论了分数阶阶数对上述现象的影响.研究发现:双频周期信号同时驱动的分数阶Dufng振子响应幅值增益Q可随着高频周期激励幅值的改变达到最大值,即出现了和整数阶非线性动力系统相似的振动共振现象,而相应的分数阶导数项则分别为系统提供了内、外两种阻尼力从而导致了系统有效势函数的改变,进而引发了比整数阶动力系统更为丰富的振动共振现象.     

Spider silk violin strings with a unique packing structure generate a soft and profound timbre

We overcome the difficulties in pulling long draglines from spiders, twist bundles of dragline filaments, and succeed in preparing violin strings. The twisting is found to change the cross section shapes of filaments from circular to polygonal and to optimize the packing structure with no openings among filaments providing mechanically strong and elastic strings. The spider string signal peaks of overtones for the violin are relatively large at high frequencies, generating a soft and profound timbre. Such a preferable timbre is considered to be due to the unique polygonal packing structure which provides valuable knowledge for developing new types of materials.     

Perceptual thresholds for detecting modifications applied to the acoustical properties of a violin

This study is the first step in the psychoacoustic exploration of perceptual differences between the sounds of different violins. A method was used which enabled the same performance to be replayed on different "virtual violins," so that the relationships between acoustical characteristics of violins and perceived qualities could be explored. Recordings of real performances were made using a bridge-mounted force transducer, giving an accurate representation of the signal from the violin string. These were then played through filters corresponding to the admittance curves of different violins. Initially, limits of listener performance in detecting changes in acoustical characteristics were characterized. These consisted of shifts in frequency or increases in amplitude of single modes or frequency bands that have been proposed previously to be significant in the perception of violin sound quality. Thresholds were significantly lower for musically trained than for nontrained subjects but were not significantly affected by the violin used as a baseline. Thresholds for the musicians typically ranged from 3 to 6 dB for amplitude changes and 1.5%-20% for frequency changes. Interpretation of the results using excitation patterns showed that thresholds for the best subjects were quite well predicted by a multichannel model based on optimal processing.     

The time-frequency characteristics of violin vibrato: modal distribution analysis and synthesis

A high-resolution time-frequency distribution, the modal distribution, is applied to the study of violin vibrato. The analysis indicates that the frequency modulation induced by the motion of the stopped finger on the string is accompanied by a significant amplitude variation in each partial of that note. Amplitude and frequency estimates for each partial are extracted from the modal distribution of ten pitches that span the range of the violin instrument. The frequency modulation is well-represented by a single sinusoid with a mean rate of 5.9 Hz and a mean excursion of +/- 15.2 cents. A spectral decomposition of the amplitude envelopes of the partials shows that the peaks lie primarily at integer multiples of the vibrato rate. These amplitude and frequency estimates are used in an additive synthesis model to generate synthetic replicates of violin vibrato. Simple approximations to these estimates are created, and synthesized sounds using these are evaluated perceptually by seven subjects using discrimination, nonmetric multidimensional scaling (MDS), and sound quality scoring tasks. It is found that the absence of frequency modulation has little effect on the perceptual response to violin vibrato, while the absence of amplitude modulation causes marked changes in both sound quality and MDS results. Low-order spectral decompositions of the amplitude and frequency estimates also occupy the same perceptual space as the original recording for a subset of the pitches studied.     

On operating deflection shapes of the violin body including in-plane motions

Earlier investigations have assumed only "out-of-plane" vibrations of the plates of the violin. The violin body can, however, be described as a thin-walled, double-arched shell structure and as such it may very well elongate in one direction as it contracts in another. Therefore, at least two orthogonal vibration components have to be included to describe the vibrations. The operating deflection shapes (ODSs) of a good, professionally made and carefully selected violin were therefore measured in several directions by TV holography to determine both "in-plane" and out-of-plane vibration components of the ODSs. The observations were limited to the frequency range 400-600 Hz, as this interval includes two most-prominent resonance peaks of bridge mobility and sound radiation as well as a third poorly radiating resonance. These three peaks clearly showed orthogonal vibration components in the ODSs. The vibration behavior of the violin body, sectioned in the bridge plane, was interpreted as the vibrations of an "elliptical tube" with nodal diameters. The number of nodal diameters increases from two to three in the selected frequency range. The TV holography measurements were supported by electrodynamical point measurements of bridge mobility, of air volume resonances, and by reciprocity, of radiation properties. Furthermore, a fourth mode, the air mode, A1, is involved indirectly in the sound radiation via influence on the body vibrations.     

Method for measuring violin sound radiation based on bowed glissandi and its application to sound synthesis

This work presents a method for measuring and computing violin-body directional frequency responses, which are used for violin sound synthesis. The approach is based on a frame-weighted deconvolution of excitation and response signals. The excitation, consisting of bowed glissandi, is measured with piezoelectric transducers built into the bridge. Radiation responses are recorded in an anechoic chamber with multiple microphones placed at different angles around the violin. The proposed deconvolution algorithm computes impulse responses that, when convolved with any source signal (captured with the same transducer), produce a highly realistic violin sound very similar to that of a microphone recording. The use of motion sensors allows for tracking violin movements. Combining this information with the directional responses and using a dynamic convolution algorithm, helps to improve the listening experience by incorporating the violinist motion effect in stereo.     

Resonance wood [Picea abies (L.) Karst.]--evaluation and prediction of violin makers' quality-grading

The definition of quality in the field of resonance wood for musical instrument making has attracted considerable interest over decades but has remained incomplete. The current work compares the traditional knowledge and practical experience of violin makers with a material-science approach to objectively characterize the properties of resonance wood. Norway spruce [Picea abies (L.) Karst.] has earned a very high reputation for the construction of resonance tops of stringed instruments and resonance boards of keyboard instruments, and was therefore chosen as the focus of the investigation. The samples were obtained from numerous renowned resonance wood regions in the European Alps and cover the whole range of available qualities. A set of acoustical, anatomical, mechanical and optical material properties was measured on each sample. These measurements were compared with subjective quality grading by violin makers, who estimated the acoustical, optical and overall suitability for violin making. Multiple linear regression models were applied to evaluate the predictability of the subjective grading using the measured material characteristics as predictors. The results show that luthiers are able to estimate wood quality related to visible features, but predictions of mechanical and acoustical properties proved to be very poor.     

The violin: Chladni patterns,plates, shells and sounds

In this article we consider the vibrations and radiated sound of the bowed violin. The vibrations are discussed in terms of the normal modes of the instrument involving the coupled vibrations of the bowed string, the supporting bridge, the hollow shell comprising the body of the instrument and, ultimately, the acoustic modes of the performance space in which the instrument is played. We show that damping plays an important role in characterizing the normal modes in what can be distinguished as weak and strong coupling limits. The historic and modern application of Chladni pattern measurements to enhance our understanding of the acoustics and as an aid to the making of violins is highlighted, alongside the modern equivalents of experimental modal and computational finite-element analysis. The symmetry-breaking properties of the internal soundpost is shown to have a profound affect on the intensity and quality of sound radiated by the bowed instrument.     

Wall compliance and violin cavity modes

Violin corpus wall compliance, which has a substantial effect on cavity mode frequencies, was added to Shaw's two-degree-of-freedom (2DOF) network model for A0 ("main air") and A1 (lowest length mode included in "main wood") cavity modes. The 2DOF model predicts a V(-0.25) volume dependence for A0 for rigid violin-shaped cavities, to which a semiempirical compliance correction term, V(-x(c)) (optimization parameter x(c)) consistent with cavity acoustical compliance and violin-based scaling was added. Optimizing x(c) over A0 and A1 frequencies measured for a Hutchins-Schelleng violin octet yielded x(c) approximately 0.08. This markedly improved A0 and A1 frequency predictions to within approximately +/- 10% of experiment over a range of about 4.5:1 in length, 10:1 in f-hole area, 3:1 in top plate thickness, and 128:1 in volume. Compliance is a plausible explanation for A1 falling close to the "main wood" resonance, not increasingly higher for the larger instruments, which were scaled successively shorter compared to the violin for ergonomic and practical reasons. Similarly incorporating compliance for A2 and A4 (lowest lower-/upper-bout modes, respectively) improves frequency predictions within +/-20% over the octet.     

Nodal line optimization and its application to violin top plate design

In the literature, most problems of structural vibration have been formulated to adjust a specific natural frequency: for example, to maximize the first natural frequency. In musical instruments like a violin; however, mode shapes are equally important because they are related to sound quality in the way that natural frequencies are related to the octave. The shapes of nodal lines, which represent the natural mode shapes, are generally known to have a unique feature for good violins. Among the few studies on mode shape optimization, one typical study addresses the optimization of nodal point location for reducing vibration in a one-dimensional beam structure. However, nodal line optimization, which is required in violin plate design, has not yet been considered. In this paper, the central idea of controlling the shape of the nodal lines is proposed and then applied to violin top plate design. Finite element model for a violin top plate was constructed using shell elements. Then, optimization was performed to minimize the square sum of the displacement of selected nodes located along the target nodal lines by varying the thicknesses of the top plate. We conducted nodal line optimization for the second and the fifth modes together at the same time, and the results showed that the nodal lines obtained match well with the target nodal lines. The information on plate thickness distribution from nodal line optimization would be valuable for tailored trimming of a violin top plate for the given performances.     

Thin walled Nb tubes for suspending test masses in interferometric gravitational wave detectors

In a previous Letter, we have shown that the use of orthogonal ribbons could provide a better mirror suspension technique in interferometric gravitational wave antennas. One of the key improvements presented by the orthogonal ribbon is the reduction in the number of violin string modes in the direction of the laser. We have considered more elaborate geometries in recent simulations and obtained a suspension that provides further reduction in the number of violin string modes in the direction of the laser, as well as in the direction orthogonal to the laser. This thin walled niobium tube suspension exhibits a reduction in the number of violin modes to 5 in each direction up to a frequency of 5 kHz. Furthermore, the violin mode thermal noise peaks can be reduced in amplitude by 30 dB.