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2023 | OriginalPaper | Buchkapitel

5. Investigating the Modal Behavior of a Violin Top and a Back Plate

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Abstract

Regarding structural dynamic behavior, the violin is a very versatile entity to study, since it combines many different effects in one single structure. Investigating this instrument means dealing with the uncertainty in natural materials, geometric nonlinearities, many interfaces, and sound radiation. Hence, this multifaceted structure serves as research subject for present work. The study starts with modal analyses of the raw spruce and maple woods, with the intention to show that an a priori material parameter identification is possible. The identified values serve as input for the orthotropic violin plates in the associated finite element model. Using 2D laser scanning vibrometry, the modal parameters are obtained for each plate. The components are supported on soft foams and on cotton wool in order to show the significant deviations in the measurement results with varying foam compliances.

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Fußnoten
1
There are two ways to manufacture violin plates: either as a solid out of one wood plate or out of two wood pieces that are glued together and then processed.
 
2
The purfling is the black inlay used to prevent cracks to develop further toward the inside of the violin plates.
 
3
The initial material parameters are based on [11].
 
Literatur
1.
Zurück zum Zitat Marshall, K.D.: Modal analysis of a violin. J. Acoust. Soc. Am. 77, 695–709 (1985)CrossRef Marshall, K.D.: Modal analysis of a violin. J. Acoust. Soc. Am. 77, 695–709 (1985)CrossRef
2.
Zurück zum Zitat Knott, G.A.: A Modal Analysis of the Violin Using MSC/NASTRAN and PATRAN. Doctoral Dissertation. Monterey, Naval Postgraduate School (1987) Knott, G.A.: A Modal Analysis of the Violin Using MSC/NASTRAN and PATRAN. Doctoral Dissertation. Monterey, Naval Postgraduate School (1987)
3.
Zurück zum Zitat Molin, N.E., Lindgren, L., Jansson, E.V.: Parameters of violin plates and their influence on the plate modes. J. Acoust. Soc. Am. 83, 281–291 (1988)CrossRef Molin, N.E., Lindgren, L., Jansson, E.V.: Parameters of violin plates and their influence on the plate modes. J. Acoust. Soc. Am. 83, 281–291 (1988)CrossRef
4.
Zurück zum Zitat Bretos, J., Santamara, C., Moral, J.A.: Vibrational patterns and frequency responses of the free plates and box of a violin obtained by finite element analysis. J. Acoust. Soc. Am. 105, 1942–1950 (1999)CrossRef Bretos, J., Santamara, C., Moral, J.A.: Vibrational patterns and frequency responses of the free plates and box of a violin obtained by finite element analysis. J. Acoust. Soc. Am. 105, 1942–1950 (1999)CrossRef
5.
Zurück zum Zitat Lu, Y.: Comparison of Finite Element Method and Modal Analysis of Violin Top Plate. Master Thesis. McGill University, Montreal (2013) Lu, Y.: Comparison of Finite Element Method and Modal Analysis of Violin Top Plate. Master Thesis. McGill University, Montreal (2013)
6.
Zurück zum Zitat Gough, C.E.: Violin plate modes. J. Acoust. Soc. Am. 137, 139–153 (2015)CrossRef Gough, C.E.: Violin plate modes. J. Acoust. Soc. Am. 137, 139–153 (2015)CrossRef
7.
Zurück zum Zitat Gough, C.E.: A violin shell model: vibrational modes and acoustics. J. Acoust. Soc. Am. 137, 1210–1225 (2015)CrossRef Gough, C.E.: A violin shell model: vibrational modes and acoustics. J. Acoust. Soc. Am. 137, 1210–1225 (2015)CrossRef
8.
Zurück zum Zitat Torres, J.A., Soto, C.A., Torres-Torres, D.: Exploring design variations of the Titian Stradivari violin using a finite element model. J. Acoust. Soc. Am. 148, 1496–1506 (2020)CrossRef Torres, J.A., Soto, C.A., Torres-Torres, D.: Exploring design variations of the Titian Stradivari violin using a finite element model. J. Acoust. Soc. Am. 148, 1496–1506 (2020)CrossRef
9.
Zurück zum Zitat Pyrkosz, M.A.: Reverse Engineering the Structural and Acoustic Behavior of a Stradivari Violin. Doctoral Dissertation. Michigan Technological University, Michigan (2013) Pyrkosz, M.A.: Reverse Engineering the Structural and Acoustic Behavior of a Stradivari Violin. Doctoral Dissertation. Michigan Technological University, Michigan (2013)
11.
Zurück zum Zitat United States Department of Agriculture, Forest Service, Forest Products Laboratory: Wood Handbook: Wood as an Engineering Material. Madison, WI :U.S. Dept. of Agriculture, Forest Service, Forest Products Laboratory (2010) United States Department of Agriculture, Forest Service, Forest Products Laboratory: Wood Handbook: Wood as an Engineering Material. Madison, WI :U.S. Dept. of Agriculture, Forest Service, Forest Products Laboratory (2010)
Metadaten
Titel
Investigating the Modal Behavior of a Violin Top and a Back Plate
verfasst von
Özge Akar
Kai Willner
Copyright-Jahr
2023
DOI
https://doi.org/10.1007/978-3-031-05445-7_5