Vibroacoustic Numerical Analisys of a Brazilian Guitar

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
• 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.
Sound Hole Plates
Neck
Block
Harmonic
Braces
Braces
Tail Block
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
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.
Wood
EL
[MPa]
Spruce 10.340
Birch 11.320
ET
[MPa]
800
880
ET
[MPa]
440
560
GLT
[MPa]
660
830
GLR
[MPa]
630
760
GRT
[MPa]
30
190
LT
0.372
0.426
LR
0.467
0.451
RT

0.435
0.697
[kg/m3]
460
668
NUMERICAL MODELLING
ACOUSTIC SYSTEM
•
•
FLUID30;
The boundary condition of null pressure is applied in the sound hole
(approximation);
Property
Density [kg/m3]
Sound Velocity [m/s]
Air
1.225
343
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 fluidstructure contact surface.
•
MODEL “A”
•
Viola caipira brand Gianinni®;
•
Suppression and compensation
internal reinforcements;
• 41,2 elements/wavelength (f = 2000Hz).
Dimensions
[mm]
a
93
b
c
102 248
d
317
e
74
f
74
of
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
2nd mode
157.55 Hz
3rd mode
212.74 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
2nd mode
264.10 Hz
3rd mode
284.20 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?