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.     

The effect of the coupling between the top plate and the fingerboard on the acoustic power radiated by a classical guitar (L)

An experimental investigation on the coupling between the fingerboard and the top plate of a classical guitar at low frequencies is presented. The study was carried out using a finished top plate under fixed boundary conditions and a commercial guitar. Radiated sound power was determined in one-third octave bands up to the band of 1 kHz based on measurements of sound intensity. The results provide evidence that the way in which the fingerboard and top plate are coupled is not a relevant factor in the radiated acoustic power of the classical guitar in the studied frequency range.     

Fourier transform microwave spectroscopy of N,N-dimethylacetamide

The jet-cooled Fourier-transform microwave spectrum of N,N-dimethylacetamide was recorded in the region of 12-24 GHz, and was analyzed to determine rotational constants and nuclear quadrupole coupling constants. Coriolis-like coupling parameters characterizing interaction between internal rotation of methyl groups and the overall rotation were also determined from internal-rotation tunneling splittings of the rotational transitions. The Coriolis-like coupling parameters permitted determination of the barrier heights to internal rotation of the three methyl groups, which were found to be 677, 237, and 183 cm⁻¹ for the C-methyl top, the trans-N-methyl top and the cis-N-methyl top, respectively.     

The computations of reflection coefficients of multilayer structure based on the reformulation of Thomson-Haskell method

A reformulation of the Thomson-Haskell method is presented for calculating the reflection coefficients of multilayer structure immersing in the coupling fluid. Instead of directly multiplying the layer propagator matrix, the new method splits the layer propagator matrix and excursively determines the interface stiffness matrix starting from the bottom half-space with known stiffness. A formulation for the reflection coefficients is derived based on the obtained interface stiffness matrix of the top layer. This scheme can be applied to a single solid layers or layered structures containing both fluid and solid layers. It keeps the simplicity but naturally excludes the exponential growth term and thus can be applied at any frequency range. Its validity and feasibility were experimentally proved by the measurement of the reflection coefficients of a three layered structure of aluminum–glass–aluminum and a sandwiched layer structure of two 250 μm stainless plates filled with 100 μm deionized water based on the inversion of V(z, t) technique. The result of experiments is consistent with the theoretical calculation. The reformulation of the Thomson-Haskell method offers an efficient and effective solution for calculating the acoustic reflection coefficients of multilayer structures of any configurations.     

Design and optimization of periodic structure mechanical filter in suppression of foundation resonances

The paper describes the development of periodic structure mechanical filter (PSMF) that has the potential to reduce vibration transmission and sound radiation at resonances of the foundation in a two-degree-of-freedom (2dof) vibration isolation system by using the band gaps of the periodic structure. The transmission matrix method is used to model vibration transmission of the 2dof system and an analytical expression of sound radiation from the foundation plate is derived. The multi-layer PSMF composed of rigid plates and curved beams is represented by an equivalent m-k-c (viscous damping) model. The propagation/attenuation zones and attenuation ability of PSMF are expressed in the propagation scenario and the iso-attenuation curves by exploiting the unit cell transfer matrix invariant. Influence of the number of unit cells, viscous damping on the mobility of PSMF and vibro-acoustic behavior of the 2dof system is extensively studied. And under the constraints of installation space and stability of the whole system, the more the number of the unit cells, the better attenuation ability in the band gap can be obtained. The interaction between PSMF and the 2dof system is analyzed by the substructure method and contribution of frequency component from different substructures is identified by setting different level of damping for each substructure. Factors influencing the first mounting frequency of the 2dof system with PSMF are discussed and three styles of installing PSMF are studied. The performance of piecewise periodic PSMF and quasi-periodic PSMF is also studied in an attempt to eliminate new-born resonances by PSMF. An optimization scheme involving sensitivity analysis is applied to obtain the optimal values of m and k. And the optimization is effective. The experiment of detecting the band gap of PSMF and the comparative trial of a 2dof system with a flexible plate as the foundation with/without PSMF are carried out. Both numerical and experimental simulation results have demonstrated that by use of PSMF, the vibration transmission at resonances is reduced and the radiation of the foundation at resonances is suppressed.     

A study of the influence of cooling water on the structural modes and vibro-acoustic characteristics of a gasoline engine

The influence of the cooling water on the vibration mode and damping characteristics of an engine was evaluated through experimental and simulation methods. The wet mode method of the fluid–structure interaction field was applied in numerical analysis, which led to several significant conclusions. Several additional fluid related modes were present when the effect of cooling water was considered. Meanwhile, the frequencies of other modes were almost the same. On the other hand, the damping characteristics of an engine were changed while the cooling water was used. For Rayleigh damping, the cooling water effect has made the mass matrix scale factor α nearly double and the stiffness matrix scale factor β almost unchanged. The engine surface vibration acceleration magnitude was calculated by means of the multi-body dynamic analysis. It was shown that the calculated vibration acceleration magnitude was close to the measured one when the cooling water was taken into account. Furthermore, acoustic simulation results were estimated by Boundary Element Method, which revealed that the sound power level of the radiation noise of most engine components was lower than that with the fluid structure interaction model being applied in the engine block modeling. The overall sound power level of the whole engine radiation noise was increased by 3.6 dB when the effect of the cooling water was considered, which demonstrated that the effect of the cooling water on the engine vibro-acoustic characteristics should not be neglected during the computation. This paper has disclosed the influences of the cooling water on the engine structural modes, damping, sound power level of the engine radiation noise and a systematic approach for evaluation of the influences.     

Acoustic and thermal properties of a cellulose nonwoven natural fabric (barkcloth)

The desire to mitigate climate change due to greenhouse gas emissions has led to the exploration of plant fibers as alternative materials for various industrial applications, sound absorption inclusive. In this investigation, sound absorption properties of Antiaris toxicaria barkcloth, and the thermal insulation properties of the barkcloth epoxy laminar composites were characterized. Theoretical sound absorption models were utilized to validate the experimental data and the empirical models were in agreement with experimental data. The lowest thermal conductivity was achieved by the Antiaris toxicaria epoxy composites.     

Ultrasound in spin glasses II

General expressions are derived for the change of the sound velocity Δv(ω,T) and the damping of sound waves γ(ω,T) in spin glasses for all temperatures and without assuming a specific spin dynamics. The calculation is based on the modulation of the exchange interactions by the sound waves. Explicit results are obtained for diffusive or relaxing spin excitations.     

Effects of surface inactivation, high temperature drying and preservative treatment on surface roughness and colour of alder and beech wood

Although extensive research has been conducted in wood surface quality analysis, a unified approach to surface quality characterisation does not exist. Measurements of the variation in surface roughness and surface colour are used widely for the evaluation of wood surface quality. Colour is a basic visual feature for wood and wood-based products. Colour measurement is one of the quality control tests that should be carried out because the colour deviations are spotted easily by the consumers. On the other hand, a common problem faced by plywood manufacturers is panel delamination, for which a major cause is poor quality glue-bonds resulting from rough veneer. Rotary cut veneers with dimensions of 500 mm × 500 mm × 2 mm manufactured from alder (Alnus glutinosa subsp. barbata) and beech (Fagus orientalis Lipsky) logs were used as materials in this study. Veneer sheets were oven-dried in a veneer dryer at 110 °C (normal drying temperature) and 180 °C (high drying temperature) after peeling process. The surfaces of some veneers were then exposed at indoor laboratory conditions to obtain inactive wood surfaces for glue bonds, and some veneers were treated with borax, boric acid and ammonium acetate solutions. After these treatments, surface roughness and colour measurements were made on veneer surfaces. High temperature drying process caused a darkening on the surfaces of alder and beech veneers. Total colour change value (ΔE^*) increased linear with increasing exposure time. Among the treatment solutions, ammonium acetate caused the biggest colour change while treatment with borax caused the lowest changes in ΔE^* values. Considerable changes in surface roughness after preservative treatment did not occur on veneer surfaces. Generally, no clear changes were obtained or the values mean roughness profile (R_a) decreased slightly in R_a values after the natural inactivation process.     

Relaxation-time analysis of second-sound data in NaF

In an earlier paper, starting from the phonon Boltzmann equation, expressions were derived which give velocityc ₂ and damping of second sound in a Debye solid in terms of mean relaxation times for various scattering processes. Using those results, heat-pulse data showing second sound in NaF were analyzed. The experimental values ofc ₂ (T) can only be reproduced if \(\bar \tau _N^{ - 1}\) , the mean relaxation rate for normal phonon collisions, varies with temperature asT ³. The mean Umklapp collision time also shows some unexpected behavior.     

阻尼耦合双层微穿孔板吸声体研究

提出并研究一种利用两板间微缝进行阻尼耦合的双层微穿孔板(DMPP)吸声体。该吸声体在两层微穿孔板(MPP)之间形成一个宽度小于1mm的微缝,因此其阻尼不仅可由板上的微穿孔提供,还可由两板之间形成的微缝提供。采用声电类比法建立了DMPP转移阻抗的理论模型,并进行实验验证,结果表明理论计算结果与实验吻合较好。然后利用建立的理论模型,对单层MPP和DMPP吸声体的吸声性能进行了对比研究,结果表明,相比于单层MPP,DMPP可以利用微缝提供的阻尼显著改善吸声性能,同时减少实际板厚。最后,对DMPP吸声体的吸声性能及其几何参数的关系进行研究,结果表明,当保持其它结构参数不变时,微缝宽度对DMPP吸声系数的提高存在一个最优值,超过或低于此值会导致吸声系数下降。     

Determination of modal coupling in vibrating rectangular plates

In square isotropic plates, some of the degenerate mode pairs are split in frequency due to coupling between longitudinal and transverse strain (which might be called Poisson coupling), and the same splitting of degenerate modes can occur in rectangular orthotropic plates having a certain length/width ratio. We have studied this coupling in free plates of aluminum and spruce (quarter cut and skew cut) and determined Poisson's ratios from the frequency ratios of the ($\text{2,0±0,2}$) modes (called the x and ring modes by luthiers). The critical length/width ratio was found to be considerably greater (3·17) in the skew-cut spruce than in quarter-cut spruce (2·08), due to a smaller cross-grain elastic modulus and Poisson's ratio.     

Phase damping destroys quantum Fisher information of W states

We study the quantum Fisher information (QFI) of W states in the basic decoherence channels. We show that, as decoherence starts and increases, under i) depolarizing, QFI smoothly decays; ii) amplitude damping, QFI first exhibits a sudden drop to the shot noise level, then decreases to zero and finally increases back to the shot noise level; iii) phase damping, QFI is zero for all non-zero decoherence. We also find that on the contrary to GHZ states, QFI of W states in x and y directions are equal to each other and zero in z direction.     

Radiation characteristics of multiple and single sound hole vihuelas and a classical guitar

Two recently built vihuelas, quasi-replicas of the Spanish Renaissance guitar, one with a small body and one sound hole and one with a large body with five sound holes, together with a classical guitar are investigated. Frequency dependent radiation strengths are measured using a 128 microphone array, back-propagating the frequency dependent sound field upon the body surface. All three instruments have a strong sound hole radiation within the low frequency range. Here the five tone holes vihuela has a much wider frequency region of strong sound hole radiation up to about 500 Hz, whereas the single hole instruments only have strong sound hole radiations up to about 300 Hz due to the enlarged radiation area of the sound holes. The strong broadband radiation of the five sound hole vihuela up to about 500 Hz is also caused by the sound hole phases, showing very consistent in-phase relations up to this frequency range. Also the radiation strength of the sound holes placed nearer to the center of the sound box are much stronger than those near the ribs, pointing to a strong position dependency of sound hole to radiation strength. The Helmholtz resonance frequency of the five sound hole vihuela is influenced by this difference in radiation strength but not by the rosettas, which only have a slight effect on the Helmholtz frequency.     

Comparative study of the photo-discoloration of moso bamboo (Phyllostachys pubescens Mazel) and two wood species

Bamboo or bamboo products undergo surface degradation during outdoor exposure resulting in lower quality in service. In this study, the effect of UV-vis light irradiation on changes in color and surface chemistry of moso bamboo (Phyllostachys pubescens Mazel) was investigated. For comparison purpose, two wood species (a soft and a hardwood) were also studied to present their differences in degradation performance. Color characterization was performed by measuring CIELab parameters (L*, a*, b* and ΔE*), and Fourier transform infrared (FTIR) spectroscopy was used to analyze the chemical changes induced by irradiation. The results showed that the surface color of bamboo changed rapidly during the irradiation process. Compared with the wood species, bamboo was less influenced by photo-irradiation. Chemical analysis indicated that irradiation altered the chemical structures of bamboo surfaces. Lignin was the most sensitive component to photo-degradation and the intensities of its characteristics bands decreased significantly during the irradiation process. This was accompanied by formation of new carbonyl groups at 1735 cm⁻¹. The rate of lignin degradation and carbonyl formation in bamboo was relatively lower compared with the wood species. The color changes (ΔE*) was well correlated with lignin degradation and carbonyl formation regardless bamboo or the wood species.     

Collective modes in charged superconductors near Tc

The dynamics of charged superconductors is described within a phenomenological model. It exhibits near T_c a screened propagating mode, which represents high frequency second sound. The damping is due to friction, to the conversion of normal to superfluid, and diffusion.     

11B magnetic resonance imaging and MAS spectroscopy of trimethylborate-treated radiata pine wood

Boron-11 nuclear magnetic resonance imaging and spectroscopy have been used to characterise the nature and distribution of boron compounds after preservative treatment of radiata pine wood with trimethylborate (TMB). One day after treatment, 11B magnetic resonance imaging microscopy showed significant differences in the morphological distribution of boron species, with there apparently being no treatment penetration of the latewood. 11B MAS NMR spectroscopy of freshly preservative-treated radiata pine wood, which had been separated into latewood and earlywood, showed the only boron species present in the latewood to be boric acid while in the earlywood both TMB and boric acid were initially present. Due to quadrupolar broadening and a short T2 value, the boric acid signal relaxed too quickly to be observable and this caused the apparent lack of 11B in the image when only boric acid was present. TMB undergoes hydrolysis to form boric acid and in radiata pine latewood, this hydrolysis reaction is rapid.     

Thermodynamic investigations of ternary o-toluidine + tetrahydropyran + N,N-dimethylformamide mixture and its binaries at 298.15, 303.15 and 308.15 K

The densities ρ, speed of sound u, data of o-toluidine (i) + tetrahydropyran (j) + N,N-dimethylformamide (k) and its {tetrahydropyran (j) + N,N-dimethylformamide (k); o-toluidine (i) + N,N-dimethylformamide (k)} binaries have been measured as a function of composition at 298.15, 303.15 and 308.15 K. The excess molar enthalpies, H^E data of same set of binary mixtures have also been measured over entire composition at 308.15 K. The densities and speeds of sound data of binary and ternary mixtures have been utilized to determine their excess molar volumes, V^E and excess isentropic compressibilities, κ_S^E. The observed thermodynamic properties of binary and ternary mixtures have been analyzed in terms of Graph theory. It has been observed that Graph theory correctly predicts the sign as well as magnitude of thermodynamic properties.     

Vibration measurements in the classical guitar

Some measurements are described that pertain to the high frequency behaviour of the vibrations of the string and soundboard of the guitar.Three isolated soundboards of different woods were compared with respect to their early decay times (by means of measurements of their vibrational impulse responses), in order to assess its possible use as an objective measure of the reverberation time of the plates. The results of all these measurements show that high frequency vibrations and radiation occurs significantly from 1 to 14 kHz, but that the sound radiation has harmonics at frequencies up to 20 kHz. This report does not produce any experimental evidence as to the importance of the high frequency region from the subjective point of view, or to the correlation of the subjective impression of reverberation of the plates with measured data of early decay times, as these aspects were not addressed at this point.     

Beyer’s non-linearity parameter (B/A) in benzylidene aniline Schiff base liquid crystalline systems

The non-linearity parameter B/A is estimated for a number of liquid crystal materials of the type N-(p-n-alkoxy benzylidene)-p-n-alkyl anilines, popularly known as nO.m, where n and m are the aliphatic chains on either side of the rigid core, which can be varied from 1 to 18 to realize a number of LC materials with a variety LC phase variants. The B/A values are computed from both density and sound velocity data following standard relations reported in literature. This systematic study in a homologous series provides an opportunity to study how this parameter behaves with (1) either the alkoxy and/or alkyl chain number, (2) with the total chain number (n+m), (3) with increase in molecular weight and (4) whether the linear relations reported in literature either with αT [thermal expansion coefficient (α) and temperature (T)] and sound velocity (u) will hold good or not and if so to what extent. The results are discussed with the body of data available in literature on liquids, liquid mixtures and other LC materials.