The setar, a Persian long-necked lute, is analyzed by means of experimental modal analysis and finite element (FE) method. The experimental analysis is performed using a combination of impulse hammer and laser Doppler vibrometer (LDV), which has led to the extraction of structural mode shapes, natural frequencies, and modal dampings. The FE model is developed taking into account structural details, such as orthotropic properties of the wood, direction of the grains, nonideal joints, and the effect of strings preload. Numerical results are shown to be in a very good agreement with the experimental data over a wide range of frequencies.

References

1.
Fletcher
,
N. H.
, and
Rossing
,
T. D.
,
1998
,
The Physics of Musical Instruments
,
Springer Verlag
,
New York
.
2.
Jansson
,
E. V.
,
2002
,
Acoustics for Violin and Guitar Makers
,
Kungl Tekniska Högskolan
,
Stockholm, Sweden
.
3.
Benade
,
A. H.
,
2012
,
Fundamentals of Musical Acoustics
,
Oxford University Press
,
New York
.
4.
Fletcher
,
N. H.
,
1999
, “
The Nonlinear Physics of Musical Instruments
,”
Rep. Prog. Phys.
,
62
(
5
), pp.
723
764
.10.1088/0034-4885/62/5/202
5.
Woodhouse
,
J.
,
Manuel
,
E.
,
Smith
,
L.
,
Wheble
,
A.
, and
Fritz
,
C.
,
2012
, “
Perceptual Thresholds for Acoustical Guitar Models
,”
Acta Acust. Acust.
,
98
(
3
), pp.
475
486
.10.3813/AAA.918531
6.
Mansour
,
H.
,
Freour
,
V.
,
Saitis
,
C.
, and
Scavone
,
G. P.
,
2015
, “
Post-Classification of Nominally Identical Steel-String Guitars Using Bridge Admittances
,”
Acta Acust. Acust.
,
101
(
2
), pp.
394
407
.10.3813/AAA.918835
7.
French
,
M.
,
2007
, “
Structural Modification of Stringed Instruments
,”
Mech. Syst. Signal Process.
,
21
(
1
), pp.
98
107
.10.1016/j.ymssp.2006.01.002
8.
Schleske
,
M.
,
2002
, “
Empirical Tools in Contemporary Violin Making: Part I. Analysis of Design, Materials, Varnish, and Normal Modes
,”
Catgut Acoust. Soc. J.
,
4
(
5
), pp.
50
64
.https://stacks.stanford.edu/file/druid:rd738kt0589/CAS_rd738kt0589.pdf
9.
Schleske
,
M.
,
2002
, “
Empirical Tools in Contemporary Violin Making: Part II. Psychoacoustic Analysis and Use of Acoustical Tools
,”
Catgut Acoust. Soc. J.
,
4
(
6
), pp.
43
61
.https://stacks.stanford.edu/file/druid:gx536qw3920/CAS_gx536qw3920.pdf
10.
Jansson
,
E. V.
,
1971
, “
A Study of Acoustical and Hologram Interferometric Measurements of the Top Plate Vibrations of a Guitar
,”
Acustica
,
25
(
2
), pp.
95
100
.http://www.ingentaconnect.com/content/dav/aaua/1971/00000025/00000002/art00007
11.
Firth
,
I. M.
,
1977
, “
Physics of the Guitar at the Helmholtz and First Top-Plate Resonances
,”
J. Acoust. Soc. Am.
,
61
(
2
), pp.
588
593
.10.1121/1.381302
12.
Stetson
,
K. A.
,
1981
, “
On Modal Coupling in String Instrument Bodies
,”
J. Guitar Acoust.
,
3
, pp.
23
31
.
13.
Marshall
,
K. D.
,
1985
, “
Modal Analysis of a Violin
,”
J. Acoust. Soc. Am.
,
77
(2), pp.
695
709
.10.1121/1.392338
14.
Jansson
,
E. V.
,
Niewczyk
,
B.
, and
Fryden
,
L.
,
1997
, “
On the Body Resonance C3 and Its Relation to the Violin Construction
,”
Catgut Acoust. Soc. J.
,
3
(3), pp.
9
14
.https://stacks.stanford.edu/file/druid:cm064cs7066/CAS_cm064cs7066.pdf
15.
Firth
,
I.
,
1976
, “
Small Mechanical Impedance Head for Use With Musical Instruments
,”
Acta Acust. Acust.
,
35
(
5
), pp.
348
349
.http://www.ingentaconnect.com/content/dav/aaua/1976/00000035/00000005/art00011
16.
Gren
,
P.
,
Tatar
,
K.
,
Granstrom
,
J.
,
Molin
,
N.
, and
Jansson
,
E. V.
,
2006
, “
Laser Vibrometry Measurements of Vibration and Sound Fields of a Bowed Violin
,”
Meas. Sci. Technol.
,
17
(
4
), pp.
635
644
.10.1088/0957-0233/17/4/005
17.
Bissinger
,
G.
, and
Oliver
,
D.
,
2007
, “
3-D Laser Vibrometry on Legendary Old Italian Violins
,”
Sound Vib.
,
41
(
7
), pp.
10
15
.http://www.sandv.com/downloads/0707biss.pdf
18.
Knott
,
G. A.
,
1987
, “
A Modal Analysis of the Violin Using MSC/NASTRAN and PATRAN
,” M.S. thesis, Naval Postgraduate School, Monterey, CA.
19.
Elejabarrieta
,
M. J.
,
Ezcurra
,
A.
, and
Santamaria
,
C.
,
2001
, “
Vibration Dynamics of the Resonance Box of the Guitar: Finite Element Method and Modal Analysis
,”
Catgut Acoust. Soc. J., Ser. II
,
4
(
4
), pp.
37
41
.https://stacks.stanford.edu/file/druid:xh244qv7083/CAS_xh244qv7083.pdf
20.
Elejabarrieta
,
M.
,
Ezcurra
,
A.
, and
Santamaria
,
C.
,
2000
, “
Evolution of the Vibrational Behavior of a Guitar Soundboard Along Successive Construction Phases by Means of the Modal Analysis Technique
,”
J. Acoust. Soc. Am.
,
108
(
1
), pp.
369
378
.10.1121/1.429470
21.
Elejabarrieta
,
M. J.
,
Ezcurra
,
A.
, and
Santamaria
,
C.
,
2002
, “
Coupled Modes of the Resonance Box of the Guitar
,”
J. Acoust. Soc. Am.
,
111
(
5
), pp.
2283
2292
.10.1121/1.1470163
22.
Elejabarrieta
,
M. J.
,
Santamaria
,
C.
, and
Ezcurra
,
A.
,
2002
, “
Air Cavity Modes in the Resonance Box of the Guitar: The Effect of the Sound Hole
,”
J. Sound Vib.
,
252
(
3
), pp.
584
590
.10.1006/jsvi.2001.3948
23.
Pyrkosz
,
M.
,
Karsen
,
C. V.
, and
Bissinger
,
G.
,
2010
, “
Converting CT Scans of a Stradivari Violin to a FEM
,” 28th International Modal Analysis Conference (
IMAC-XXVIII
), Jacksonville, FL, Feb. 1–4, pp.
811
820
.10.1007/978-1-4419-9834-7_71
24.
Pyrkosz
,
M. A.
, and
Van Karsen
,
C.
,
2014
, “
Coupled Vibro-Acoustic Model of the Titian Stradivari Violin
,”
Topics in Modal Analysis I
, Vol.
7
,
Springer
,
New York
, pp.
317
332
.
25.
Gough
,
C. E.
,
2015
, “
Violin Plate Modes
,”
J. Acoust. Soc. Am.
,
137
(
1
), pp.
139
153
.10.1121/1.4904544
26.
Gough
,
C. E.
,
2015
, “
A Violin Shell Model: Vibrational Modes and Acoustics
,”
J. Acoust. Soc. Am.
,
137
(
3
), pp.
1210
1225
.10.1121/1.4913458
27.
Feng
,
S.
,
1984
, “
Some Acoustical Measurements on the Chinese Musical Instrument P'i-P'a
,”
J. Acoust. Soc. Am.
,
75
(
2
), pp.
599
602
.10.1121/1.390533
28.
Yoshikawa
,
S.
,
Shinoduka
,
M.
, and
Senda
,
T.
,
2008
, “
A Comparison of String Instruments Based on Wood Properties: Biwa Vs. Cello
,”
Acoust. Sci. Technol.
,
29
(
1
), pp.
41
50
.10.1250/ast.29.41
29.
Damodaran
,
A.
,
Mansour
,
H.
,
Lessard
,
L.
,
Scavone
,
G.
, and
Babu
,
A. S.
,
2015
, “
Application of Composite Materials to the Chenda, an Indian Percussion Instrument
,”
Appl. Acoust.
,
88
, pp.
1
5
.10.1016/j.apacoust.2014.07.013
30.
Peekna
,
A.
, and
Rossing
,
T. D.
,
2005
, “
The Acoustics of Carved Baltic Psalteries
,”
Acta Acust. Acust.
,
91
(
2
), pp.
269
276
.http://www.ingentaconnect.com/content/dav/aaua/2005/00000091/00000002/art00009
31.
Waltham
,
C.
, and
Kotlicki
,
A.
,
2008
, “
Vibrational Characteristics of Harp Soundboards
,”
J. Acoust. Soc. Am.
,
124
(
3
), pp.
1774
1780
.10.1121/1.2956479
32.
Mansour
,
H.
,
Kasaiezadeh
,
A.
,
Arzanpour
,
S.
, and
Behzad
,
M.
,
2009
, “
Finite Element Modeling of Setar, a Stringed Musical Instrument
,”
ASME
Paper No. IMECE2009-13015. 10.1115/IMECE2009-13015
33.
Gough
,
C. E.
,
2007
,
Springer Handbook of Acoustics
,
Springer Verlag
,
New York
, Chap. 15.
34.
Bank
,
B.
, and
Sujbert
,
L.
,
2005
, “
Efficient Modeling Strategies for the Geometric Nonlinearities of Musical Instrument Strings
,” Forum Acusticum 2005, Budapest, Hungary, Aug. 29-Sept. 2, pp. 691–696.
35.
Ewins
,
D. J.
,
2000
,
Modal Testing: Theory, Practice and Application
,
Research Studies Press
,
Baldock, Hertfordshire, UK
.
36.
Bissinger
,
G.
,
1995
, “
Some Mechanical and Acoustical Consequences of the Violin Soundpost
,”
J. Acoust. Soc. Am.
,
97
(5), pp.
3154
3164
.10.1121/1.411876
37.
Bissinger
,
G.
, and
Keiffer
,
J.
,
2003
, “
Radiation Damping, Efficiency, and Directivity for Violin Normal Modes Below 4 kHz
,”
Acoust. Res. Lett. Online
,
4
(
1
), pp.
7
12
.10.1121/1.1524623
38.
Nikolaidis
,
E.
, and
Lee
,
K.
,
1992
, “
A 3-D Joint Model for Automotive Structures
,”
SAE
Technical Paper No. 921088.10.4271/921088
39.
Ezcurra
,
A.
,
Elejabarrieta
,
M.
, and
Santamaria
,
C.
,
2005
, “
Fluid-Structure Coupling in the Guitar Box: Numerical and Experimental Comparative Study
,”
Appl. Acoust.
,
66
(
4
), pp.
411
425
.10.1016/j.apacoust.2004.07.010
40.
Mansour
,
H.
, and
Behzad
,
M.
, “
An Experimental Study to Find the Acoustic Quality Indicators of Mulberry Wood
,”
ASME
Paper No. IMECE2010-38388.10.1115/IMECE2010-38388
41.
Mansour
,
H.
,
Scavone
,
G.
, and
Freour
,
V.
, “
A Comparison of Vibration Analysis Techniques Applied to the Persian Setar
,”
Acoustics 2012
, Nantes, France, Apr. 23–27, pp.
1737
1742
.http://www.music.mcgill.ca/caml/lib/exe/fetch.php?media=publications:nantes2012_mansour.pdf
42.
Woodhouse
,
J.
,
2002
, “
Body Vibration of the Violin—What Can a Maker Expect to Control?
,”
Catgut Acoust. Soc. J., Ser. II
,
4
(
5
), pp.
43
49
.https://stacks.stanford.edu/file/druid:rd738kt0589/CAS_rd738kt0589.pdf
43.
Woodhouse
,
J.
, and
Langley
,
R.
,
2012
, “
Interpreting the Input Admittance of Violins and Guitars
,”
Acta Acust. Acust.
,
98
(
4
), pp.
611
628
.10.3813/AAA.918542
44.
Weinreich
,
G.
,
Holmes
,
C.
, and
Mellody
,
M.
,
2000
, “
Air-Wood Coupling and the Swiss-Cheese Violin
,”
J. Acoust. Soc. Am.
,
108
(5), pp.
2389
2402
.10.1121/1.1314397
You do not currently have access to this content.