Research Papers

Modal Analysis of the Setar: A Numerical–Experimental Comparison

[+] Author and Article Information
Hossein Mansour

Computational Acoustic Modeling Laboratory,
Schulich School of Music,
McGill University,
555 Sherbrooke Street West,
Montréal, QC H3A 1E3, Canada
e-mail: hossein.mansour@mail.mcgill.ca

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 26, 2015; final manuscript received June 10, 2015; published online July 14, 2015. Assoc. Editor: Nicole Kessissoglou.

J. Vib. Acoust 137(6), 061006 (Dec 01, 2015) (7 pages) Paper No: VIB-15-1099; doi: 10.1115/1.4030863 History: Received March 26, 2015; Revised June 10, 2015; Online July 14, 2015

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.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Fletcher, N. H., and Rossing, T. D., 1998, The Physics of Musical Instruments, Springer Verlag, New York.
Jansson, E. V., 2002, Acoustics for Violin and Guitar Makers, Kungl Tekniska Högskolan, Stockholm, Sweden.
Benade, A. H., 2012, Fundamentals of Musical Acoustics, Oxford University Press, New York.
Fletcher, N. H., 1999, “The Nonlinear Physics of Musical Instruments,” Rep. Prog. Phys., 62(5), pp. 723–764. [CrossRef]
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. [CrossRef]
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. [CrossRef]
French, M., 2007, “Structural Modification of Stringed Instruments,” Mech. Syst. Signal Process., 21(1), pp. 98–107. [CrossRef]
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
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
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
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. [CrossRef]
Stetson, K. A., 1981, “On Modal Coupling in String Instrument Bodies,” J. Guitar Acoust., 3, pp. 23–31.
Marshall, K. D., 1985, “Modal Analysis of a Violin,” J. Acoust. Soc. Am., 77(2), pp. 695–709. [CrossRef]
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
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
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. [CrossRef]
Bissinger, G., and Oliver, D., 2007, “3-D Laser Vibrometry on Legendary Old Italian Violins,” Sound Vib., 41(7), pp. 10–15. [CrossRef]
Knott, G. A., 1987, “A Modal Analysis of the Violin Using MSC/NASTRAN and PATRAN,” M.S. thesis, Naval Postgraduate School, Monterey, CA.
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
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef]
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. [CrossRef]
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.
Gough, C. E., 2015, “Violin Plate Modes,” J. Acoust. Soc. Am., 137(1), pp. 139–153. [CrossRef] [PubMed]
Gough, C. E., 2015, “A Violin Shell Model: Vibrational Modes and Acoustics,” J. Acoust. Soc. Am., 137(3), pp. 1210–1225. [CrossRef] [PubMed]
Feng, S., 1984, “Some Acoustical Measurements on the Chinese Musical Instrument P'i-P'a,” J. Acoust. Soc. Am., 75(2), pp. 599–602. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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
Waltham, C., and Kotlicki, A., 2008, “Vibrational Characteristics of Harp Soundboards,” J. Acoust. Soc. Am., 124(3), pp. 1774–1780. [CrossRef] [PubMed]
Mansour, H., Kasaiezadeh, A., Arzanpour, S., and Behzad, M., 2009, “Finite Element Modeling of Setar, a Stringed Musical Instrument,” ASME Paper No. IMECE2009-13015. [CrossRef]
Gough, C. E., 2007, Springer Handbook of Acoustics, Springer Verlag, New York, Chap. 15.
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.
Ewins, D. J., 2000, Modal Testing: Theory, Practice and Application, Research Studies Press, Baldock, Hertfordshire, UK.
Bissinger, G., 1995, “Some Mechanical and Acoustical Consequences of the Violin Soundpost,” J. Acoust. Soc. Am., 97(5), pp. 3154–3164. [CrossRef]
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. [CrossRef]
Nikolaidis, E., and Lee, K., 1992, “A 3-D Joint Model for Automotive Structures,” SAE Technical Paper No. 921088. [CrossRef]
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. [CrossRef]
Mansour, H., and Behzad, M., “An Experimental Study to Find the Acoustic Quality Indicators of Mulberry Wood,” ASME Paper No. IMECE2010-38388. [CrossRef]
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
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. [CrossRef]
Woodhouse, J., and Langley, R., 2012, “Interpreting the Input Admittance of Violins and Guitars,” Acta Acust. Acust., 98(4), pp. 611–628. [CrossRef]
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. [CrossRef] [PubMed]


Grahic Jump Location
Fig. 1

Schematic view of the setar

Grahic Jump Location
Fig. 2

CAD model of the setar, mostly measured by CMM

Grahic Jump Location
Fig. 3

Assembly of the soundbox, different shades (color version is online) represent element groups with different thicknesses. The row of elements on the edge of the bowl is to simulate the nonideal glue between the bowl and the plate.

Grahic Jump Location
Fig. 4

Structure of the bowl composed of different ribs, bent, and glued together

Grahic Jump Location
Fig. 5

Model of the bridge, all the nodes at the bottom surface of the bridge are connected to the coincident nodes on the plate with spring–damper elements acting normal to the plate, except for the nodes marked with filled circles which are merged to the coincident nodes on the plate

Grahic Jump Location
Fig. 6

A sample measured mobility on the setar's plate

Grahic Jump Location
Fig. 7

Experimental setup used to extract the structural FRFs: impulse hammers strike on the bridge and LDV measures velocity on the plate

Grahic Jump Location
Fig. 8

Mode shapes and natural frequencies of the plate obtained from the experimental and numerical results, compared together. The setar was clamped on its neck.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In