The modal behaviour of a violin corpus

Abstract

Violins incorporate numerous interfaces and anisotropic behaviour due to natural materials. Hence, the modelling of these instruments is extremely complex. The present work investigates the structural dynamics of a specific violin corpus (violin resonant body) with the aim of using numerical modelling to accurately understand the modal behaviour of the violin using a novel stepwise approach. In the first step, an inverse material parameter identification via experimental and numerical modal analysis of the raw woods is performed to obtain the material parameters of the individual woods. In the second step, an experimental modal analysis of the violin substructures is performed using 2D scanning laser Doppler vibrometry and building finite element models based on accurate 3D scans of the parts manufactured by a luthier. The experimentally obtained modal parameters of the individual parts are compared with the numerical results. In the third step, the whole violin corpus, i.e. the resonant body of the instrument, is assessed. The good agreement between the numerical and the experimental results demonstrates that the application of standard techniques of modal analysis on a very complex mechanical system, the violin body, is possible. Our methodology offers a novel approach to analysing individual components of bowed string instruments, facilitating a comprehensive vibrational analysis with implications for broader musical research, including luthier optimisation tools, digital reconstruction of historical violins, and advancements in instrument design for improved playability and tonal quality.

KEYWORDS:

• Violin
• Modal analysis
• Finite elements
• Laser-Doppler vibrometry
• Digital twin

Acknowledgements

We would like to express our sincere gratitude to the luthiers Bernd Dimbath and Günter Waldau at Heinrich Gill GmbH, D-91094 Langensendelbach,⁸ for manufacturing the violin. We would also like to thank the NAF Neunkirchener Achsenfabrik AG, D-91077 Neunkirchen am Brand,⁹ for performing and providing the 3D scans of the violin components.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Bernd Dimbath and Günter Waldau at Heinrich Gill GmbH.

2 The steps are as follows: raw wood, free plates, top plate with bass bar and bottom plate with ribs and the complete corpus.

3 URL https://www.maul-theet.com/.

4 In other words, the test structure was oscillating for a long time, which is impracticable when more than 800 points need to be measured; i.e. each point is hit 3 times; hence, 2400 measurements are performed.

5 URL https://www.gom.com/.

6 URL https://www.meshlab.net/.

7 URL https://www.beta-cae.com/ansa.htm.

8 URL http://heinrichgill.com/.

9 URL https://www.nafaxles.com/.