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![Equal-loudness contours [red: ISO 226:2003 revision, blue: ISO 226:1987 for 40 phons].](publication/311940189/figure/fig6/AS:1086741956046891@1636110881923/Equal-loudness-contours-red-ISO-2262003-revision-blue-ISO-2261987-for-40-phons.jpg)
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![Monopole sound radiation from 3-degree-of-freedom model [4].](publication/311940189/figure/fig3/AS:1086741956042845@1636110881707/Monopole-sound-radiation-from-3-degree-of-freedom-model-4_Q320.jpg)
![Isolated oscillator resonances for Kohno classical guitar [10].](publication/311940189/figure/fig4/AS:1086741956042848@1636110881756/Isolated-oscillator-resonances-for-Kohno-classical-guitar-10_Q320.jpg)
![Phase relationship for Kohno classical guitar [10].](publication/311940189/figure/fig5/AS:1086741956038705@1636110881840/Phase-relationship-for-Kohno-classical-guitar-10_Q320.jpg)
Research has shown that the soundboard plays an increasingly important role compared to the sound hole, back plate, and the bridge at high frequencies. The frequency spectrum of investigation can be extended to 5 kHz. Design of bracings and their placements on the soundboard increase its structural stiffness as well as redistributing its deflection...
Citations
... The guitar is a plucked musical instrument that is known for its artistic, health, and psychological benefits, as well as its ability to enhance human creativity [2][3][4][5][6]. Knowledge of sound analysis and synthesis is important for understanding and manipulating the guitar's sound [7,8]. The guitar produces periodic sounds from the plucking of its strings, which can be described using Fourier series [9,10]. ...
This research aims to analyze and synthesize periodic signals derived from guitar string plucking with hammer-on technique. This research has three stages, namely the data collection stage, the analysis stage, and the synthesis stage. The guitar string was plucked with a tension of 2.5 N and recorded using a sound sensor connected to PASCO Capstone software. The data used has two variations, namely the sound signal of a hammer-on pluck with a half tone increase and a one tone increase. Data analysis was carried out using MATLAB software to obtain deviation graphs as a function of frequency, damping coefficient values, and frequency spectra. The results showed that after hammer-on the amplitude of the tone decreased drastically as the mass per unit length of the string decreased. The initial tone before the hammer-on will appear in the tone after the hammer-on with a lower amplitude as the mass per unit length of the string increases. The synthesis of guitar sounds with this technique is done by combining the individual tones obtained and adjusting the time interval and amplitude according to the literature data
... Further, the work by Meng Koon Lee et al. in [5] talks about the physical modeling based on the interaction of the strings of the guitar with other parts of the guitar body. The researchers experimented with the sound generated by guitar with respect to soundboard and its relationship with the guitar body. ...
Music is the pulse of human lives and is an amazing tool to relieve and re-live. And when it comes to the signal processing, impulse is the pulse of the researchers. The work presented here is focused on impulse response modeling of noted produced by box shaped acoustic guitar. The impulse response is very fundamental behavior of any system. The music note is the convolution of the impulse response and the excitation signal of that guitar. The frequency of the generated music note follows the octave rule. The octave rule can be checked for impulse responses as well. If the excitation signal and impulse response are separated, then an impulse response of a single fret can be used to generate the impulse responses of other frets. Here the music notes are analyzed and synthesized on the basis of the plucking style and plucking expression of the guitar-player. If the impulse response of the musical instrument is known, the output music note can be synthesized in an unusual manner. Researchers have been able to estimate the impulse response by breaking the string of the guitar. Estimating the impulse response from the recorded music notes is possible using the methodology of cepstral domain window. By means of the Adaptive Cepstral Domain Window (ACDW) the author estimated the impulse response of guitar notes. The work has been further extended towards the classification of synthesized notes for plucking style and plucking expression using Neural Network and Machine Learning algorithms.
... There is some literature on numerical modelling that extends to higher frequency [7], but much of the literature is concentrated on measurements of mode shapes and sound fields, and increasingly elaborate numerical models: see for example [8][9][10]. The recent review article [11] gives many other literature references. Guitar makers can manipulate these low modes through constructional details, especially the chosen material, mass and bracing pattern for the soundboard [12,13]. ...
Measurements of vibrational response of an American 5-string banjo and of the sounds of played notes on the instrument are presented, and contrasted with corresponding results for a steel-string guitar. A synthesis model, fine-tuned using information from the measurements, has been used to investigate what acoustical features are necessary to produce recognisable banjo-like sound, and to explore the perceptual salience of a wide range of design modifications. Recognisable banjo sound seems to depend on the pattern of decay rates of “string modes”, the loudness magnitude and profile, and a transient contribution to each played note from the “body modes”. A formant-like feature, peaking around 500–800 Hz on the banjo tested, is found to play a key role. At higher frequencies the dynamic behaviour of the bridge produces additional formant-like features, reminiscent of the “bridge hill” of the violin, and these also produce clear perceptual effects.
... investigaram o comportamento dinâmico de um violão clássico (violão de Torres) ao longo de diferentes estágios de construção por meio de análise modal experimental e numérica, empregando elementos finitos, simulação computacional, medidas de frequências naturais e modos de vibrar (técnica de Chladni) da caixa de ressonância por meio de excitação mecânica.O emprego da modelagem computacional é focado na resolução de problemas em várias áreas da ciência tais como: social, ambiental, engenharia,climática, etc. Nessa abordagem é possível antecipar desempenhos, eventualmente detectar falhas, enfim prever o comportamento em condições mais abrangentes que aquelas possíveis de serem realizadas em laboratórios(Curtu et al., 2008;Lee et al., 2018). O método de elementos finitos, assim como diversas outras soluções matemáticas, é uma ferramenta numérica que permite prevê problemas de contorno(Lotti et al., 2006 apud Melo et al., 2020. ...
Um violão é construído essencialmente de madeira. Porém, cada madeira traz consigo algumas características específicas. O seu comportamento acústico está relacionado às propriedades elásticas dos materiais que o compõem. Sabe-se que as propriedades elásticas dos materiais interferem não apenas em sua resistência mecânica, mas também em seu comportamento dinâmico; uma estrutura pode vibrar de forma mais ou menos intensa dependendo do material que a compõe e de suas propriedades elásticas. O presente trabalho analisa o comportamento dinâmico de um modelo computacional de violão através de análises modais calculadas pelo método de elementos finitos (MEF) aplicando condições de contorno que simulam a rigidez das faixas laterais e a tensão das cordas no cavalete e braço obtendo respostas em termos de frequências naturais e as correspondentes formas dos modos de vibração. E assim, comparar com respostas em frequência obtidas experimentalmente através do método de excitação por impulso. Os resultados mostram que as respostas em frequências naturais numéricas se assemelham com os valores obtidos experimentalmente, indicativo de pertencerem a um mesmo modo de vibração.
... The plates were edge-constrained as shown in Fig. 4a. Figure 4b shows the structural elements. The dynamic response of the plate is obtained based on Kirchhoff's hypotheses and applying the d'Alembert principle or another energy method, Eq. (4) (Lee et al. 2016;Stanciu et al. 2019): ...
The aim of this article is to correlate the experimental modal analysis (EMA) with finite element analysis (FEA) to study the effect of wood species on vibration modes of violin plates made of spruce and maple. For EMA, five violin plates each made of spruce and maple were tested (curly maple, quilted maple, common maple with regular and irregular rings). The plates were clamped on edges and subjected to forced vibration. Experimental Chladni patterns of these plates were determined for 36 emitted frequencies, range between 65 and 2637 Hz. Patterns obtained with modal analysis are characterised by the nodal lines. The patterns of vibration modes are affected by wood species and structure. Spruce plate shows nodal lines aligned to the longitudinal (L) anisotropic direction of wood, corresponding to the direction of the fibres. Maple plates show nodal lines aligned to radial (R) anisotropic direction of wood and to the direction of medullary rays in the LR plane. Curly maple plate vibration produced the best resolution of vibration modes pattern, because of the presence of very abundant medullary rays, well oriented in the R direction. Quilted maple plate has asymmetric modes of vibration. At the highest frequency of 2093 Hz, no vibrating zones were observed during the experiment. Maple plates of normal structure with regular and irregular annual rings have shown similar patterns, but differ from curly maple plate. The characteristics of annual rings were measured. The vibrating surfaces (Sv) of the plates obtained experimentally were measured by transferring the nodal lines into AutoCAD 2013 software, where the surfaces were computed and expressed in mm2 or in % of the total surface area of the plate; the total effective vibrating surface for all frequencies for each plate and wood species; the relative vibrating surface at maximum amplitude. The experimental results were compared to modal analysis performed with FEA, by using ABAQUS program. The similar geometry of the real plates was generated in ABAQUS and the violin plates were meshed with quadratic shell elements. The plates were modelled as orthotropic materials. At maximum vibration amplitude and frequency of 110 Hz, the spruce plate has a relative vibrating surface of 62%, a mean annual ring width of 0.77 mm and ring heterogeneity of only 64%. At maximum amplitude of vibration and frequency of 174 Hz, the plates made of curly maple LR and LT (longitudinal–tangential), have different behaviour. The vibrating surface is greater for the plate made of curly maple LR with dense figures (84%) and annual ring heterogeneity of 86%, than for plates made of curly maple LT with large figures (77%) and annual ring heterogeneity of 238%.
... Thus, there is a close connection between the parts of the guitar as a mechanical structure that ensures the propagation of vibrations from the strings (the excitation system) to the guitar body. From a dynamic point of view, the guitar body behaves like a Helmholz resonator [39][40][41]. It was noticed that a basic condition of the resonance boxes of the guitar is that of not being selective, respectively, of not favoring some sounds. ...
... In the technological process of producing the manufactured guitars, various bar systems are used, depending on the type, size and quality of the guitar in which they are integrated. The number of scientific studies on how the stiffening system influences the acoustic quality of the guitar is relatively low [16,26,40,53], and the studies are generally not exhaustive, given the interaction of the many factors that contribute to the acoustic quality of the guitar. Moreover, the approaches aim to analyze aspects of the particular bar systems. ...
Wood is a natural composite, having a porous structure, with a complex elastic symmetry specific to orthotropic solid, influenced by three mutually perpendicular planes of elastic symmetry. The classical guitar is obtained from different wooden species, each of them having their own elastic properties and, as a whole, forming a lignocellulosic composite structure. Generally, some constructive parts of the classical guitar body are based on symmetry, starting from the structural features of wooden plates, which are symmetrically cut, and some patterns of the stiffening bars. The other elements, such as the strings system, are not symmetric. This study aims to evaluate the frequency responses of the guitar body as a symmetrical mechanical system from constructive points of view. Because theoretical results (analytic and numeric) regarding the symmetrical systems cannot be applied to quasi-symmetric systems, the dynamic response was analyzed from experiments performed on four types of classical guitar body (without neck), different from each other by the pattern of stiffening bars placed inside of the top plate. The experiments were performed using a Brüel&Kjær mini-shaker to excite the structure, and the signal was captured with accelerometers. The symmetric behavior of coupled plates from the guitar body was noticed in the case of an applied dynamic force of 110 Hz and 440 Hz, but in the case of 146 Hz, 588 Hz, 720 Hz, quasi skew symmetrical modes were recorded.
... In the paper the object of the main theoretical interest is the structure of plates with different degrees of complexity and with various stiffening systems [21][22][23]. Based on Kirchhoff's hypotheses and applying the d'Alembert principle or another energy method, it is obtained the dynamic response of the plate [23,24]: ...
This paper aimed to use the symmetry that exists to the body of a guitar to ease the analysis behavior to vibrations. Symmetries can produce interesting properties when studying the dynamic and steady-state response of such systems. These properties can, in some cases, considerably decrease the effort made for dynamic analysis at the design stage. For a real guitar, these properties are used to determine the eigenvalues and eigenvectors. Finite element method (FEM) is used for a numerical modeling and to prove the theoretically determined properties in this case. In this paper, different types of guitar plates related to symmetrical reinforcement patterns were studied in terms of modal analysis performed using finite element analysis (FEA). The dynamic response differs in terms of amplitude, eigenvalues, modal shapes in accordance with number and pattern of stiffening bars. In this study, the symmetrical and asymmetric modes of modal analysis were highlighted in the case of constructive symmetrical structures.
... The implication of the simulated support is that it allows unlimited motion of the irregular-shaped plate in the x-and y-directions compared to the simple support of the analytical model and hence affects the magnitudes of the natural frequencies for higher modes. It is worthy to note that control of natural frequencies is also possible with the use of scalloped braces 6,26,27 . ...
An irregular-shaped plate with dimensions identical to a guitar soundboard is chosen for this study. It is well known that the classical guitar soundboard is a major contributor to acoustic radiation at high frequencies when compared to the bridge and sound hole. This paper focuses on using an analytical model to compute the sound power of an unbraced irregular-shaped plate of variable thickness up to frequencies of 5 kHz. The analytical model is an equivalent thin rectangular plate of variable thickness. Sound power of an irregular-shaped plate of variable thickness and with dimensions of an unbraced Torres' soundboard is determined from computer analysis using ANSYS. The number of acoustic elements used in ANSYS for accurate simulation is six elements per wavelength. Here we show that the analytical model can be used to compute sound power of an unbraced irregular-shaped plate of variable thickness.
... Case study: soundboard of a classical guitar Research in acoustic radiation has shown that the soundboard plays an increasingly important role compared to the bridge and sound hole of classical guitars as frequency increases, Bader [29] . Current research on increasing acoustic radiation of this musical instrument involve redistributing the natural frequencies of the soundboard using scalloped braces, bracing design and the splitting board, as well as mathematical modelling of the complete instrument, Lee et al. [30] . An important parameter in the study of acoustic radiation of materials is the absorption coefficient. ...
The Homotopy Perturbation Method (HPM) was developed to search for asymptotic solutions of nonlinear problems involving parabolic partial differential equations with variable coefficients. This paper illustrates that HPM be easily adapted to solve parabolic partial differential equations with constant coefficients. Natural frequencies of a rectangular plate of uniform thickness, simply-supported on all sides, are obtained with minimum amount of computation. The solution is shown to converge rapidly to a combination of sine and cosine functions. Truncating the series solution by using only the first three terms of the sine and cosine functions as compared to the exact solution results in an absolute error not exceeding 2 × 10⁻⁴ and 9 × 10⁻⁴ for the trigonometric functions respectively. HPM is then applied to solve the nonlinear problem of a rectangular plate of variable thickness. A direct expression for the eigenvalues (natural frequencies) of the rectangular plate is obtained as compared to determining its eigenvalues by solving the characteristic equation using the conventional method. Comparison of results for the frequency parameter with existing literature show that HPM is highly efficient and accurate. Natural frequencies of a simply-supported guitar soundboard were obtained using an equivalent rectangular plate with the same boundary condition.
The large wooden resonator of the Sarasvati Veena amplifies and radiates the sound in almost all directions. The directional and spatial dependence of this radiation is studied in conjunction with the mode shapes of the top plate of the resonator. Sound radiation patterns are simulated theoretically using the nodal displacement data obtained from the numerical modal analysis of the resonator. The experimental analysis involves the manual plucking of the Veena string. The radiated sound is recorded by placing microphones around the resonator in circular arrays of different radii in the different planes. These combinations of arrays at different distances and planes provide a thorough knowledge of sound radiating out of the resonator. The intensities of different frequencies in the recorded spectral data as functions of direction and distance from the approximate center of the top plate of the resonator are studied. Experimentally measured patterns show the importance of the top plate over the body of the resonator. Theoretical and experimental radiation patterns for different harmonics of the plucked string are compared and a good match is observed. The behavior of the radiating sound in the different planes at different radial distances from the assumed center is discussed.
