Archives of Acoustics, 44, 1, pp. 35–49, 2019
10.24425/aoa.2019.126350

Modelling and Measurement of Folk Guitar: Truss Rod and Strings in Numerical Analysis of Tone

Paweł Michał BIELSKI
http://bielski.edu.pl
Gdansk University of Technology
Poland

Marcin KUJAWA
Gdansk University of Technology
Poland

Izabela Katarzyna LUBOWIECKA
Gdansk University of Technology
Poland

The study makes an attempt to model a complete vibrating guitar including its non-linear features, specifically the tension-compression of truss rod and tension of strings. The purpose of such a model is to examine the influence of design parameters on tone. Most experimental studies are flawed by uncertainties introduced by materials and assembly of an instrument. Since numerical modelling of instruments allows for deterministic control over design parameters, a detailed numerical model of folk guitar was analysed and an experimental study was performed in order to simulate the excitation and measurement of guitar vibration. The virtual guitar was set up like a real guitar in a series of geometrically non-linear analyses. Balancing of strings and truss rod tension resulted in a realistic initial state of deformation, which affected the subsequent spectral analyses carried out after dynamic simulations. Design parameters of the guitar were freely manipulated without introducing unwanted uncertainties typical for experimental studies. The study highlights the importance of acoustic medium in numerical models.
Keywords: sound quality; musical instruments; acoustic folk guitar; string tension; truss rod; non-linear modelling
Full Text: PDF

References

Arnold D.N. (2001), A concise introduction to numerical analysis, Institute for Mathematics and its Applications, Minneapolis.

Bathe K.-J., Wilson E.L. (1976), Numerical methods in finite element analysis, Prentice-Hall Englewood Cliffs, NJ.

Bécache E., Chaigne A., Derveaux G., Joly P. (2005), Numerical simulation of a guitar, Computers & Structures, 83, 2, 107–126.

Bielski P., Kujawa M. (2017), Nonlinear modelling in time domain numerical analysis of stringed instrument dynamics, AIP Conference Proceedings, Vol. 1822, AIP Publishing, p. 020003.

Bissinger G., Hutchins C. (1983), Further evidence for coupling between plate and enclosed air vibrations in string instruments, Catgut Acoustical Society Newsletter, 40, 18–19.

Bissinger G., Keiffer J. (2003), Radiation damping, efficiency, and directivity for violin normal modes below 4 khz, Acoustics Research Letters Online, 4, 1, 7–12.

Brémaud I. (2012), Acoustical properties of wood in string instruments sound boards and tuned idiophones: Biological and cultural diversity, The Journal of the Acoustical Society of America, 131, 1, 807–818.

Brémaud I., Minato K., Thibaut B. (2009), Mechanical damping of wood as related to species classification: a preliminary survey, 6th Plant Biomechanics Conference PBM09, pp. 536–542, Cayenne, French Guiana.

Campbell M., Greated C. (1994), The musician's guide to acoustics, Oxford University Press, Oxford.

Derveaux G., Chaigne A., Joly P., Bécache E. (2003), Time-domain simulation of a guitar: Model and method, The Journal of the Acoustical Society of America, 114, 6, 3368–3383.

Duerinck T., Skrodzka E., Linde B.B. (2014), Modal analysis of a trapezoidal violin built after the description of félix savart, Archives of Acoustics, 39, 4, 623–628.

Elejabarrieta M., Ezcurra A., Santamaria C. (2002), Coupled modes of the resonance box of the guitar, The Journal of the Acoustical Society of America, 111, 5, 2283–2292.

Ezcurra A., Elejabarrieta M., Santamaria C. (2005), Fluid–structure coupling in the guitar box: numerical and experimental comparative study, Applied Acoustics, 66, 4, 411–425.

Falk R.H., Itani R.Y. (1987), Dynamic characteristics of wood and gypsum diaphragms, Journal of Structural Engineering, 113, 6, 1357–1370.

Fletcher N.H., Rossing T. (2012), The physics of musical instruments, Springer Science & Business Media, New York.

Fritz C., Cross I., Moore B.C., Woodhouse J. (2007), Perceptual thresholds for detecting modifications applied to the acoustical properties of a violin, The Journal of the Acoustical Society of America, 122, 6, 3640–3650.

Gore T. (2011), Wood for guitars, Proceedings of Meetings on Acoustics 161ASA, Vol. 12, ASA, p. 035001.

Green D.W., Winandy J.E., Kretschmann D.E. (1999), Mechanical Properties of Wood, [in:] Wood Handbook: Wood as an Engineering Material, Forest Products Laboratory, Madison, WI, pp. 4-4–23.

Helmholtz H. (1954), On the Sensations of Tone as a Physiological Basis for the Theory of Music, 2nd edition, Dover Publications Inc., New York, trans. A. Ellis.

Inácio O., Antunes J., Wright M. (2008), Computational modelling of string–body interaction for the violin family and simulation of wolf notes, Journal of Sound and Vibration, 310, 1, 260–286.

Irvine T. (2004), Damping properties of materials, https://syont.files.wordpress.com/2007/05/damping-properties-of-materials.pdf.

Issanchou C., Bilbao S., Le Carrou J.-L., Touzé C., Doaré O. (2017), A modal-based approach to the nonlinear vibration of strings against a unilateral obstacle: Simulations and experiments in the pointwise case, Journal of Sound and Vibration, 393, 229–251.

Jackman C., Zampino M., Cadge D., Dravida R., Katiyar V., Lewis J. (2009), Estimating acoustic performance of a cell phone speaker using Abaqus, SIMULIA Customer Conference, pp. 14–21, London, England.

Jansson E.V. (2002), Acoustics for violin and guitar makers, Kungl Tekniska högskolan, Department of Speech, Music and Hearing, Stockholm.

Khennane A., Khelifa M., Bleron L., Viguier J. (2014), Numerical modelling of ductile damage evolution in tensile and bending tests of timber structures, Mechanics of Materials, 68, 228–236.

Kopač J., Šali S. (1999), The frequency response of differently machined wooden boards, Journal of sound and vibration, 227, 2, 259–269.

Lemoine T.J., McMillin C.W., Manwiller F.G. (1970), Wood variables affecting the friction coefficient of spruce pine on steel, Wood Science, 2, 3, 144–148.

Liu M., Gorman D. (1995), Formulation of rayleigh damping and its extensions, Computers & Structures, 57, 2, 277–285.

Lynch C., Woodhouse J., Langley R. (2013), Sound radiation from point driven shell structures, Journal of Sound and Vibration, 332, 26, 7089–7098.

Mansour H., Fréour V., Saitis C., Scavone G.P. (2015), Post-classification of nominally identical steel-string guitars using bridge admittances, Acta Acustica united with Acustica, 101, 2, 394–407.

McLennan J. (2003), A0 and A1 studies on the violin using CO2, He, and air/helium mixtures, Acta Acustica united with Acustica, 89, 1, 176–180.

Meier E. (n.d.), The Wood Database, Retrieved November 7th, 2016 form www.wood-database.com.

Mottola R.M. (2007), Sustain and electric guitar neck joint type, American Lutherie, 91, 52.

Okuda A., Ono T. (2008), Bracing effect in a guitar top board by vibration experiment and modal analysis, Acoustical Science and Technology, 29, 1, 103–105.

Ono T., Okuda A. (2007), Acoustic characteristics of guitars with a top board of carbon fiber-reinforced composites, Acoustical Science and Technology, 28, 6, 442–443.

Runnemalm A. (1999), Standing waves in a rectangular sound box recorded by TV-holography, Journal of Sound and Vibration, 224, 4, 689–707.

Russell D. (1998), Modal analysis of an acoustic folk guitar, Kettering University, Applied Physics, Flint, MI, acs.psu.edu/drussell/guitars/hummingbird.html.

Sauer R.A., Luginsland T. (2017), A monolithic fluid-structure interaction formulation for solid and liquid membranes including free-surface contact, arXiv preprint arXiv:1710.02128.

Skrodzka E., Krupa A., Rosenfeld E., Linde B.J. (2009), Mechanical and optical investigation of dynamic behavior of violins at modal frequencies, Applied Optics, 48, 7, C165.

Skrodzka E., Łapa A., Linde B.B.J., Rosenfeld E. (2011), Modal parameters of two incomplete and complete guitars differing in the bracing pattern of the soundboard, The Journal of the Acoustical Society of America, 130, 4, 2186–2194.

Skrodzka E., Linde B.B.J., Krupa A. (2014), Effect of bass bar tension on modal parameters of a violin's top plate, Archives of Acoustics, 39, 1, 145–149.

Skrodzka E.B., Linde B.B., Krupa A. (2013), Modal parameters of two violins with different varnish layers and subjective evaluation of their sound quality, Archives of Acoustics, 38, 1, 75–81.

Sproßmann R., Zauer M., Wagenführ A. (2017), Characterization of acoustic and mechanical properties of common tropical woods used in classical guitars, Results in Physics, 7, 1737–1742.

Torres J. (2010), The bridge, modes of vibration and sound radiation in middle frequencies of the classical guitar [in Spanish: El puente, modos de vibración y radiación sonora en frecuencias medias de la guitarra clásica], Ph.D. thesis, Universidad Nacional Autónoma de México.

Torres J.A., Boullosa R.R. (2009), Influence of the bridge on the vibrations of the top plate of a classical guitar, Applied Acoustics, 70, 11, 1371–1377.

Torres J.A., Torres-Martínez R. (2015), Evaluation of guitars and violins made using alternative woods through mobility measurements, Archives of Acoustics, 40, 3, 351–358.

Vegte G. van der, Makino Y. (2004), Numerical simulations of bolted connections: the implicit versus the explicit approach, Proceedings of the 5th International Workshop on Connections in Steel Structures, pp. 89–98, Amsterdam, The Netherlands.

Wegst U.G. (2006), Wood for sound, American Journal of Botany, 93, 10, 1439–1448.

Weinreich G., Holmes C., Mellody M. (2000), Air-wood coupling and the swiss-cheese violin, The Journal of the Acoustical Society of America, 108, 5, 2389–2402.

Wolfe J. (n.d.a), Helmholtz Resonance, Retrieved October 18th, 2016 from The University of New South Wales, http://newt.phys.unsw.edu.au/jw/Helmholtz.html.

Wolfe J. (n.d.b), Music Acoustics, Retrieved October 18, 2016 from The University of New South Wales, http://newt.phys.unsw.edu.au/music/.

Woodhouse J., Manuel E., Smith L., Wheble A., Fritz C. (2012), Perceptual thresholds for acoustical guitar models, Acta Acustica united with Acustica, 98, 3, 475–486.

Xiaoming C., Jin D., Yungui L. (2015), Mass proportional damping in nonlinear time-history analysis, 3rd International Conference on Material, Mechanical and Manufacturing Engineering (IC3ME 2015), pp. 567–571, Guangzhou, China.

Zienkiewicz O.C., Taylor R.L. (1977), The finite element method, Vol. 3, McGraw-Hill, London.

Zoran A., Welch S., Hunt W.D. (2012), A platform for manipulation and examination of the acoustic guitar: The chameleon guitar, Applied Acoustics, 73, 4, 338–347.




DOI: 10.24425/aoa.2019.126350

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