The structural analyses of classical guitar body through experimental methods.

Curtu, Ioan ; Stanciu, Mariana Domnica ; Nastac, Silviu 等

1. INTRODUCTION

In classical guitar construction are used different braces systems of top plates. The number, material and pattern of stiffening braces influence the mass and stiffness of structure which leads to different dynamical responses of gutiar bodies. The dynamical behaviour of lignocelluloses box is directly linked by acoustical ones.

The aim of experimental research is to establish the dynamical behaviour of each type of guitar body in terms of Chladni patterns and resonance frequencies, through experimental method.

2. LITERATURE REVIEW

The previous studies of authors (Curtu & Stanciu, 2008, 2009) are focused on finite element analyses of guitar plates, bodies as individual structures and in conjunction with neck. The results were comparable with references as Elejabarrieta et all (2007) who studied the modal analysis and vibration behavior of the classical guitar in different construction stages using FEM, Richardson (1983) who performed studies on classical guitar to establish the influence of individual features on the modal shapes and frequency, Becache et all (2004) who studied the time-domain numerical modelling of the fluid--structure interaction of guitar and Bader (2005) which approaches brought into focus the physical sounds of the instruments from a musicological point of view.

3. MATERIALS AND METHOD

In the case of the undertaken research were studied 4 types of classical guitar bodies: case 1--body with top plate with three transversal bars (hence 3BT), case 2--five radial braces and 2 transversal braces (hence 5BR), case 3--with 7 radial braces and 2 transversal braces (hence 7BR) and case 4--with 3 radial braces and 2 in V position (hence 3BR2V). The types of sample are presented in Fig. 1. The material of top plates was resonance spruce, the back and sides was made from maple.

[FIGURE 1 OMITTED]

In order to study the influences of stiffening braces, the guitar body without its neck was investigated through numerical and experimental method (Curtu, 2009). The used method consisted of applying a harmonic excitation to the structures by means of the mini-shaker. The experimental stand was built according to the scheme in Fig. 2. Each guitar body (5) was freely supported on a foam device (4) and excited with a B&K mini-shaker (2) located on a bridge area of the top plate. The frequencies of harmonic force: 82, 110, 146.83, 196, 246.9, 329.2, 440, 588, 720, 980 Hz generated through frequency generator. The input signal was measured with a force transducer (3) and the forced vibrations of each structure (the output signal) were captured with three B&K 4517-002 type accelerometers (6) (measuring on z direction). The recording and processing of signals in time and in frequency domain it was performed by means of B&K Pulse 12 system (7) connected to the personal computer (8). To determine the modal shapes, the top plate of guitar body was covered with a thin uniform sand layer with 100-150 grit size.

[FIGURE 2 OMITTED]

4. RESULTS AND DISCUSSION

4.1 Chladni patterns

The modal shapes of top plates knowing as Chladni pattern are given by the distribution of the significant nodal lines on the surface of structure. The nodal line represents the points or areas which remain in equilibrium position during the vibration. During vibrations, each pattern of strutting system characteristically has nodes and antinodes at various locations on the body of the guitar. There are many methods to determine the Chladni patterns: non contact--holographic interferometer techniques and with contact--using powder covered of plate. In this research we used the second technique as it can be seen in Fig. 3. Comparing the obtained results it can be noticed that there are a lot of similarities regarding the modal shapes of low frequencies (110, 146, 196 Hz). With increasing of frequency, the Chladni patterns become more complex and different from a structure to another (Fig. 3). The 5BR an 7BR guitar bodies have the same modal shapes and modes with sensitive differences in terms of clarity of shapes.

[FIGURE 3 OMITTED]

4.2 The analyses in time and frequency domain

As it was mentioned in the first part, to record and process data the soft program of Pulse System B&K was used (Fig. 4). The processed signals of each measurement were displayed in numerous charts. Some of them are presented in paper.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

First, it could be noticed that the dynamical behaviour of guitar body regardless of strutting system is governed by the same harmonic law as excitation force. In spite of the same values of harmonic excitations which were applied during the experiments, it was recorded different resonance frequencies for acoustic bodies of classical guitar with different braces pattern. The guitar body type 5BR, 7BR and 3BR2V recorded similarly values, in all range of resonance frequencies (low, medium and high frequencies). The 3BT type responded starting with medium resonance frequencies, but the centroid of values is between 616 and 976 Hz. Experimental researches show that 5BR and 3BR2V guitar types have common resonance frequencies. In Fig. 5 are presented comparisons between experimental results and theoretical ones obtained with FEM. There are many similarities between them.

5. CONCLUSION

The experimental investigation of different types of classical guitar bodies has been performed to establish the structural differences reflected on dynamical behaviour of them. Due to the anisotropic materials from guitar structure as is wood, the results varied even the same strutting system of top plate. The approach presented in this paper is focused on structural analyses. It was neglected the influence of bridge and guitar neck. The results show that the increasing of stiffness of top plate from guitar body conduct to a structural modification visible in frequency responses of structure. The obtained data are useful for further studies which aim to optimize the guitar body taking into account the proper ratio between resistance and vibration characteristics of top plate.

6. ACKNOWLEDGEMENT

This work was accomplished under the following grants: PNII71-016 MODIS, project responsible prof. dr. eng. Curtu Ioan, University Transilvania of Brasov, and CNCSIS Bucuresti TD cod 182, no. 222/2007, project manager Stanciu Mariana Domnica, University Transilvania of Brasov.

7. REFERENCES

Bader, R.: (2005). Computational Mechanics of the Classical Guitar, Springer-Verlag Berlin Heidelberg N.Y., in Netherland, 2005, ISBN 3-540-25136-7

Becache, E.; Chaigne, A.; Derveaux, G. & Joly, P. (2005). Numerical simulation of a guitar, Computers and Structures, Vol 83, 2005, pp 107-126

Curtu I., Stanciu M. D. & Savin A. (2008). The propagation of forced vibrations in coupled plates of guitars, Proceeding of the 19th International DAAAM Symposium "Intelligent Manufacturing & Automation: Focus on Next Generation of Intelligent Systems and Solutions", Katalinic, B. (Ed) ISSN 1726-9679, Trnava, Slovacia 22-25 Octombrie 2008, pp 345-346

Curtu I, Stanciu M, Cretu N & Rosca I (2009). Modal Analysis of Different Types of Classical Guitar Bodies, Proceedings of the 10th WSEAS International Conference on Acoustics & Music: Theory & Applications--AMTA09, 23-25 March 2009, Prague, Czech Republic, ISBN: 978-960-474-061-1, ISSN: 1790-5095, pp 30-34

Elejabarrieta, M. J.; Ezcurra, A. & Santamaria, C. (2007). Resonance Box of the Guitar Structure-Fluid Interaction, Proceeding of 19th International Congress on Acoustics Madrid, 2-7 september 2007, http://www.sea-acustica.es

Richardson, B. E. & Roberts, G. (1983). The adjustment of mode frequencies in guitars: a study by means of holographic interferometry and finite element analysis, Proc. Stockholm Music Acoustics Conference, Pub. Royal Swedish Academy of Music, 46 (2), 285-302