Vibroacoustic Numerical Analisys of a

Brazilian Guitar Resonance Box

José Maria Campos dos Santos (zema@fem.unicamp.br)

Guilherme Orelli Paiva (pitupaiva@fem.unicamp.br)

University of Campinas, UNICAMP-FEM-DMC,

Rua Mendeleyev, 200 , Cidade Universitária "Zeferino Vaz",

Campinas, SP –Brazil

INTRODUCTION

• Currently, an important aspect of research in the acoustic of

musical instruments is to relate measurable physical

properties of an instrument with the subjective evaluation of

its sound quality or tone;

• The use of numerical models to determine the vibration

modes, which influence the desired tone of a musical

instrument, seems to be a valuable tool to its project;

• This work uses numerical modal analysis, calculated by

finite element method (FEM), to determine the dynamic

behavior of a Brazilian guitar resonance box.

THE BRAZILIAN GUITAR

• The Brazilian guitar is a countryside

musical instrument. It has different

characteristics that vary regionally. This

work is focused on the Viola Caipira

(Redneck Guitar), which is the most

known and played in all regions of Brazil;

• The Viola Caipira is derived from the

Portuguese guitar, which originates in

Arabic instruments like the lute.

SOURCE: Corrêa, Roberto. A Arte de Pontear Viola. Brasília/Curitiba: 1ª ed. 2000.

THE BRAZILIAN GUITAR

Braces

Sound Hole Plates

Harmonic Braces

Neck Block

Tail Block

• The stiffness of soundboard must be

enough to withstand the traction on the

strings over the bridge;

• The rigidity of the resonance box is

modified by fixing internal

reinforcements.

NUMERICAL MODELLING

• Structural System: soundboard + back plate +

sides + reinforcements;

• Acoustic System: air cavity + sound hole;

• Vibroacoustic System: coupling between

structural and acoustic systems.

NUMERICAL MODELLING

• The finite element computer models of the resonance box

were built in the software (Mechanical APDL –

Release 13.0);

• The geometries of the models were constructed from the

main dimensions of commercial instruments;

• The difficulty to identify the wood of resonance box

components led to the choices by indications from the

literature;

• Frequency range: 0 – 2000 Hz

NUMERICAL MODELLING

Wood EL

[MPa]

ET

[MPa]

ET

[MPa]

GLT

[MPa]

GLR

[MPa]

GRT

[MPa]

LT LR RT

[kg/m3]

Spruce 10.340 800 440 660 630 30 0.372 0.467 0.435 460

Birch 11.320 880 560 830 760 190 0.426 0.451 0.697 668

STRUCTURAL SYSTEM

• Wood is best described as an orthotropic material;

SHELL63: soundboard, back plate and sides;

BEAM188: internal reinforcements and bridge;

Soundboard and internal reinforcements:

Sitka Spruce wood;

Back plate and sides:

Yellow Birch wood.

NUMERICAL MODELLING

ACOUSTIC SYSTEM • FLUID30;

• The boundary condition of null pressure is applied in the sound hole

(approximation);

VIBROACOUSTIC SYSTEM • The vibroacoustic model considers the resonance box structure filled with air;

• Fluid-structure interaction is obtained with the coupling matrices, which lead to a

solution of an eigenproblem with asymmetric matrices (unsymmetric extraction

method);

• The ANSYS imposes this condition through the FSI command applied in fluid-

structure contact surface.

Property Air

Density [kg/m3] 1.225

Sound Velocity [m/s] 343

MODEL “A”

Dimensions

[mm]

a b c d e f

93 102 248 317 74 74

• Viola caipira brand Gianinni®;

• Suppression and compensation of

internal reinforcements;

• 41,2 elements/wavelength (f = 2000Hz).

MODEL “A”

Structural mesh: 8.820 elements and 8.831 nodes

Acoustic mesh: 33.920 elements and 38.467 nodes

MODEL “A”

Results

• Qualitative correlation between

coupled and uncoupled modes;

• Sometimes predominance of

structural modes, sometimes

predominance of acoustic

modes.

MODEL “A”

1st mode

114.35 Hz

3rd mode

212.74 Hz

2nd mode

157.55 Hz

4th mode

232.17 Hz

MODEL “B”

• Viola Caipira brand Rozini®;

• Include internal reinforcements and

bridge;

• In order to compare the experimental

results with the numerical ones, the

computational model was updating

varying the mechanical properties of

woods (elastic modules and density);

• 22,0 elements/wavelength (f= 2000Hz).

MODEL “B”

MODEL “B”

Structural mesh: 6149 elements e 12253 nodes

Acoustic mesh: 16128 elements and 19242 nodes

MODEL “A”

1st mode

154.62 Hz

3rd mode

284.20 Hz

2nd mode

264.10 Hz

4th mode

349.02 Hz

MODEL “B”

• Experimental verification: Chladni Technique

MODEL “B”

MODEL “B”

CONCLUSIONS

• MODEL “A”: Was verified qualitatively the correlation between coupled and

uncoupled modes. Sometimes predominate structural modes, sometimes

predominate acoustic modes;

• MODEL “B”: In general, it was observed that these fluid-structure finite element

formulation proved to be effective and can determine the dynamic behavior of the

resonance box of the guitar, especially for the first modes;

• The technique of Chladni figures reveals clearly only the experimental modes

with enough power to push the particles of tea to the nodal lines;

•The disagreement between some results can be attributed to the simplifications

assumed in computer simulation (mechanical properties). Also, the lacquer layer

and presence of the neck that were not considered in the computational model.

THANK YOU!

Questions?