Evolution of the vibrational behavior of a guitar soundboard along successive construction phases by means of the modal analysis technique

The crucial piece of a craft guitar is the soundboard since it determines the quality of the sound given by the instrument. From the initial phase (the gross plate with no hole) until the last construction phase (the plate with the full structure) several stages are followed to modify the dynamic behavior of the structure and hence the acoustic response of the final guitar. The aim of this work is to analyze the effect of each modification on the vibrational response of the plate. With this in mind, an experimental modal analysis of all the construction phases has been performed in the low frequency range under free conditions. The response of the plate in each stage is defined by vibration patterns, resonance frequencies, quality factors, and admittance curves.     

Vibroacoustic characteristics of a gothic harp

The "gothic" style of harp was popular across most of Europe from the late medieval period to the Renaissance. These harps have a one-piece, longitudinally oriented hardwood soundboard, as opposed to the transverse-oriented bonded softwood structure on a modern instrument. In addition, the one-piece back is flexible, whereas the back of a modern instrument is a rigid molded shell. To study the gothic harp, one was constructed from plans created by the Boston Museum of Fine Arts from a late German model in their collection. The vibrational behaviors of the soundboard and soundbox were measured at various stages of construction. The completed instrument was subjected to modal analysis and radiativity measurements. The sound radiation is dominated by two breathing modes at 188 and 273 Hz, each with strong motion of the back, and modes around 350 Hz. Taken together, these modes function like the A0/T1 resonance pairs seen in the soundboxes of other instruments, and a comparison is made with the guitar. Also observed is that as the frequency increases, radiation is emitted from higher up the soundboard, and from higher soundholes. This feature has been observed in other harps, and is a consequence of the harp family's unique geometry.     

Acoustics of the jarana jarocha

Some acoustical measurements on the jarana jarocha primera (first), a traditional Mexican instrument, a “one-piece” body instrument, in the coastal region of the Gulf of Mexico, are presented. Experimental mobility function, radiativity function, and some radiation patterns were obtained. Harmonic analysis and visualization techniques using both the finite element method and laser speckle-Chladni methods were made to obtain the lower deflection shapes of the soundboard. The experimental analysis using mobility function measurements of the lower resonances shows behaviour very similar to that observed in the classical guitar.     

Physics-based modeling techniques of a twelve-string Portuguese guitar: A non-linear time-domain computational approach for the multiple-strings/bridge/soundboard coupled dynamics

The Portuguese guitar is a pear-shaped instrument with twelve metal strings which is widely used in Portuguese traditional music. Unlike most common guitars, it has a curved top-plate and a specific violin-like bridge which is not rigidly fixed to the soundboard of the instrument. From the dynamical point of view, if the bridge transmits the strings vibrations to the instrument body in order to maximize the radiated energy, it also couples all the component parts of the instrument which therefore interact by structural coupling. This can originate various audible effects such as beating behavior and the excitation of numerous sympathetic resonances enhanced by the large number of strings of the instrument, and this is certainly why the Portuguese guitar has such distinct sound compared to other guitars. In this paper, a fully coupled time-domain model of the Portuguese guitar is developed and a series of simulations are presented to emphasize the various coupling phenomena involved in sound production. To reproduce the main musical features, the model includes the coupled dynamics of the twelve strings supported by a bridge which interact with the body of the instrument, described through Finite-Element modeling of the soundboard of a typical Portuguese guitar. Further simple models have been devised for the string/fret interaction and the pluck excitation. Since nonlinear effects are quite apparent in the behavior of string musical instruments, the string dynamics is modeled by the Kirchhoff–Carrier equations which describe large-amplitude string vibrations, and includes the coupling between both polarizations of string motion. The coupling between the strings and the soundboard at the bridge is provided by a model of the bridge kinematics, built on the basis of simple geometrical rationale, so that the two perpendicular string motions can exchange energy back and forth. By a close examination of the energy transfers between the various subsystems of the model, we first assess the correct behavior of the physical model and then examine the respective influence of the string nonlinearity and the bridge on the nonplanar motion of the string. The fully coupled model which pertains to the restricted group of studies which deals with the complete physical-based modeling of a multi-stringed instrument, captures many important phenomena observed in practice, among which the pitch glide effect and the mutual excitation of sympathetic vibrations.     

Experimental study of AO and T1 modes of the concert harp

String instruments are usually composed of a set of strings, a soundboard, and a soundbox with sound holes, which is generally designed to increase the sound level by using the acoustic resonances of the cavity. In the case of the harp, the soundbox and especially the sound holes are primarily designed to allow access to the strings for their mounting. An experimental modal analysis, associated to measurements of the acoustic velocity in the holes, shows the importance of two particular modes labeled A0 and T1 as it was done for the guitar and the violin. Their mode shapes involve coupled motions of the soundboard's bending and of the oscillations of the air pistons located in the sound holes. The A0 mode is found above the frequency of the lowest acoustically significant structural mode T1. Thus, the instrument does not really take advantage of the soundbox resonance to increase its radiated sound in low frequencies. However, contribution of mode A0 is clearly visible in the response of the instrument, confirming the importance of the coupling between the soundboard and the cavity.     

体声波力传感器灵敏度的微分-综合分析法

为了分析基于应力/应变效应的体声波(BAW)力传感器的敏感机理、准确计算其灵敏度,提出了一种用于BAW力传感器灵敏度分析的微分-综合分析法。该方法借鉴了微积分的原理,在Mason等效电路模型中将一个完整的BAW谐振器替换为多个谐振器微元的并联,从而将谐振器有源区面积A上应力/应变场的有限元计算结果与压电薄膜材料的力学特性、谐振器微元的电声学特性关联起来;最后,在射频电路仿真软件中进行等效电路的综合,得到整个BAW谐振器在应力/应变场作用下的阻抗特性曲线及其串/并联谐振频率。当BAW谐振器微元的划分足够细密时,获得的灵敏度分析结果将足够精确。为了论证该方法的原理,给出了一个直观的校核案例。以一个嵌入式FBAR结构的四梁BAW加速度计表头为例,介绍了该方法用于BAW力传感器灵敏度分析的详细过程。虽然案例中只讨论了一种应力/应变型BAW力传感器的单一力敏机理,但该方法具有普适性。并且,当谐振器微元小到接近其压电材料晶格的尺度时,就能与压电薄膜的力-声-电特性的第一性原理计算结果关联起来,实现从微观材料特性到介观器件物理的多尺度计算。     

The application of smart structures toward feedback suppression in amplified acoustic guitars

Smart structures technology can be applied to amplified acoustic guitars to prevent instability resulting from acoustic feedback. This work presents a coupled model of the guitar dynamics and the acoustic feedback mechanism, and explains how a simple control loop using a piezoelectric ceramic actuator can be used to reduce the effects of acoustic feedback. In addition to model simulations, experimental results using a real system and a simple controller are presented. The results show that a significantly higher (7 dB) guitar output can be achieved before instability, without detrimentally affecting the amplified and unamplified guitar response.     

A frequency selective acoustic transducer for directional Lamb wave sensing

A frequency selective acoustic transducer (FSAT) is proposed for directional sensing of guided waves. The considered FSAT design is characterized by a spiral configuration in wavenumber domain, which leads to a spatial arrangement of the sensing material producing output signals whose dominant frequency component is uniquely associated with the direction of incoming waves. The resulting spiral FSAT can be employed both for directional sensing and generation of guided waves, without relying on phasing and control of a large number of channels. The analytical expression of the shape of the spiral FSAT is obtained through the theoretical formulation for continuously distributed active material as part of a shaped piezoelectric device. Testing is performed by forming a discrete array through the points of the measurement grid of a scanning laser Doppler vibrometer. The discrete array approximates the continuous spiral FSAT geometry, and provides the flexibility to test several configurations. The experimental results demonstrate the strong frequency dependent directionality of the spiral FSAT and suggest its application for frequency selective acoustic sensors, to be employed for the localization of broadband acoustic events, or for the directional generation of Lamb waves for active interrogation of structural health.     

Optical sensors based on Fabry–Perot resonator and fringes of equal thickness structure

We propose theoretically two optical sensor structures based on Fabry–Perot resonator and fringes of equal thickness structure. Different from the conventional slab waveguide sensors in which the sample interacts with the evanescent field in the cladding layer, the proposed sensors contain the sample in the core layer. The first proposed sensor comprises a piezoelectric material as a substrate with the driving potential difference as the sensing probe for refractive index changes of the sample. The second sensor comprises fringes of equal thickness structure with the number of fringes per unit length is the probe for changes in the index of the sample. The calculations reveal that the proposed sensors have high sensitivity to changes in the refractive index of the sample.     

Force–frequency effect of thickness mode langasite resonators

Langasite resonators are of recent interest for a variety of applications because of their good temperature behavior, good piezoelectric coupling, low acoustic loss and high Q factor. The force–frequency effect describes the shift in resonant frequency a resonator experiences due to the application of a mechanical load. A clear understanding of this effect is essential for many design applications such as pressure sensors. In this article, the frequency shift is analyzed theoretically and numerically for thin, circular langasite plates subjected to a pair of diametrical forces. In addition, the sensitivity of the force–frequency effect is analyzed with respect to the nonlinear material constants. The results are anticipated to be valuable for experimental measurements of nonlinear material constants as well as for device design.     

Eignmodes of piezoelectric lenses

Conclusion The generalized expressions obtained for calculating eigenfunctions of harmonic and nearby anharmonic modes of a PEL make it possible better to direct the search for optimal resonator geometry. These functions enable us to compute such equivalent dynamic parameters of resonators as the inductance, capacitance, capacitance ratio, and others. They also enable us to determine resonator sensitivity to a localized change in PE thickness, which is proportional to the square of the eigenfunction; this is necessary not only in the manufacture of resonators, but in the construction of various kinds of piezoelectric sensors as well.Translated from Izvestiya Vysshikh Uchebnykh Uchebnykh Zavedenii, Radiofizika, Vol. 29, No. 6, pp. 740–747, June 1986.     

Theoretical analysis of a quartz-enhanced photoacoustic spectroscopy sensor

Quartz-enhanced photoacoustic spectroscopy (QEPAS) sensors are based on a recent approach to photoacoustic detection which employs a quartz tuning fork as an acoustic transducer. These sensors enable detection of trace gases for air quality monitoring, industrial process control, and medical diagnostics. To detect a trace gas, modulated laser radiation is directed between the tines of a tuning fork. The optical energy absorbed by the gas results in a periodic thermal expansion which gives rise to a weak acoustic pressure wave. This pressure wave excites a resonant vibration of the tuning fork thereby generating an electrical signal via the piezoelectric effect. This paper describes a theoretical model of a QEPAS sensor. By deriving analytical solutions for the partial differential equations in the model, we obtain a formula for the piezoelectric current in terms of the optical, mechanical, and electrical parameters of the system. We use the model to calculate the optimal position of the laser beam with respect to the tuning fork and the phase of the piezoelectric current. We also show that a QEPAS transducer with a particular 32.8 kHz tuning fork is 2–3 times as sensitive as one with a 4.25 kHz tuning fork. These simulation results closely match experimental data.     

Numerical shape optimization of photoacoustic resonators

The sensitivity of photoacoustic sensors strongly depends on the shape of the acoustical resonator. Up to now, mainly photoacoustic sensors consisting of a number of cylindrical parts have been investigated (cylinder cells, H cells, T cells etc.). In this paper, a numerical shape optimization of the resonator cell of photoacoustic sensors is described. The approach considers all shapes that can be represented by a number of axisymmetrical truncated cones which are connected in a continuous way. In addition, the geometry of the cell is subjected to certain constraints, e.g.  the laser beam should not be blocked during its passage through the cell. The purpose is to maximize the sensor’s signal strength. The acoustic pressure at the position of the microphone represents the objective function and is calculated using an eigenmode expansion combined with a finite element calculation. The solution of a 17-dimensional nonlinear optimization problem is a resonator shape with a substantial quality improvement with reference to the well-known H cell.     

Vibrational behavior of a soundbox in an atmosphere with a variable speed of sound

This paper describes a semi-quantitative method, suitable for a student laboratory exercise that shows that the acoustic properties of the soundbox of a musical instrument depend on the sound speed of the atmosphere surrounding and filling the instrument. A gas tent was constructed and used to enclose instruments in helium, carbon dioxide and mixtures thereof, allowing the sound speed to be varied from 250 to 1000 m/s. Soundboard admittance data were taken using a guitar and a violin as examples. The data, expressed as contour plots, show clearly the qualitative relationship between air and wood modes, and the guitar data are compared with a simple mechanical model. Experimental details of the construction and operation of gas tent are given, with attention paid to safety issues.     

用于矢量水听器的低频高灵敏度层合梁加速度传感器

压电加速度传感器是同振型矢量水听器的核心部件。为了满足低频高灵敏度矢量水听器的应用需求,提出并研究一种具有层合梁结构的低频高灵敏度加速度传感器。结合弹性力学和压电方程推导层合梁加速度传感器的加速度灵敏度解析解表达式,通过有限元仿真对层合梁加速度传感器尺寸进行优化,给出优化后的尺寸范围。从优化的尺寸范围中选取两种不同尺寸进行加速度传感器振动特性的仿真分析及实物制作(其中压电材料为PZT-5)与性能测试。仿真与测试结果均表明,相比已有的同尺寸金属梁加速度传感器,层合梁加速度传感器可以有效降低谐振频率并提升加速度灵敏度。当压电层厚度为0.5 mm时,加速度灵敏度最大提升3.9 dB,谐振频率下降23%。测试结果与理论分析相符。      

Fatigue behaviour and structural health monitoring by acoustic emission of E-glass/epoxy laminates with piezoelectric implant

This paper represents the continuation of our research on built-in piezoelectric sensor for structural health monitoring of composite materials. Experimental research is focused on examining the effects of the embedded sensors on the structural integrity of composite laminates subjected to mechanical tests. A series of composite specimens with and without embedded sensor are tested in fatigue loading while constantly monitoring the response by acoustic emission technique. The acoustic signals are analysed using the classification k-means method in order to identify the different damage mechanisms and to follow the evolution of these mechanisms for both types of composite materials (with and without sensor). The mechanical behaviour of composites with and without embedded sensor shows no difference in the form. The incorporation of piezoelectric sensor causes low degradation of mechanical properties of composites. Comparing embedded sensor to sensor mounted on the surface, the embedded sensor showed a much higher sensitivity. It is thus verified that the embedded acoustic emission sensor had great potential for acoustic emission monitoring in fibre reinforced composite structures.     

Some characteristics of the concert harp's acoustic radiation

The way a musical instrument radiates plays an important part in determining the instrument's sound quality. For the concert harp, the soundboard has to radiate the string's vibration over a range of 7 octaves. Despite the effort of instrument makers, this radiation is not uniform throughout this range. In a recent paper, Waltham and Kotlicki [J. Acoust. Soc. Am. 124, 1774-1780 (2008)] proposed an interesting approach for the study of the string-to-string variance based on the relationship between the string attachment position and the operating deflection shapes of the soundboard. Although the soundboard vibrational characteristics determine a large part of the instrument's radiation, it is also important to study directly its radiation to conclude on the origins of the string-to-string variation in the sound production. This is done by computing the equivalent acoustical sources on the soundboard from the far field sound radiation measured around the harp, using the acoustic imaging technique inverse frequency response function. Results show that the radiated sound depends on the correlation between these sources, and the played string's frequency and location. These equivalent sources thus determine the magnitude and directivity of each string's partial in the far field, which have consequences on the spectral balance of the perceived sound for each string.     

Efficient intensity modulation due to surface acoustic waves on windows of the AlGaN/InGaN multiple quantum well laser

An alternative method for modulation of light generated by AlGaN/InGaN multiple quantum well laser with quartz antireflective (AR) coatings covering the resonator windows was modelled and studied theoretically. Disturbance of the piezoelectric coatings caused by surface acoustic waves (SAW) results in efficient intensity modulation of the laser beam. The model for the laser diode operating at DC demonstrates that the modulation factor can exceed 0.2 in sub-nanometer SAW displacement. For quarter-wave AR films, the carrier frequency of modulated beam has twice the frequency of SAW.