# Fluid-structure-acoustic interaction problem in modelling of human vocal folds vibration

## Main Article Content

## Abstract

This paper studies vibroacoustic sound produced by self-oscillating human vocal folds model as one of major sound source responsible for human phonation. The human phonation is a complex phenomenon described by interaction of three physical fields -- elastic body deformation, fluid flow and acoustics, and their mutual couplings. Therefore it is sometimes referred as fluid-structure-acoustic interaction (FSAI) problem. Here we present FSI problem modelled by linear elasticity theory (vocal fold) and the viscous incompressible airflow modelled by Navier-Stokes equations due to typical low flow velocities of small Mach number. The arbitrary Lagrangian-Euler method (ALE) for the purpose of numerical simulation of the time varying computational domain is applied. In order to model one sound source mechanism of the human phonation the vibroacoustic problem is solved in larger acoustic domain including vocal tract model. The sound source considered in this model is the normal acceleration of the vibrating vocal folds boundary. The numerical models are based on the finite element method. The results of vibroacoustic problem are shown and analyzed.

## Article Details

How to Cite

Valášek, J., Sváček, P., & Horáček, J.
(2020).
Fluid-structure-acoustic interaction problem in modelling of human vocal folds vibration.

*Proceedings Of The Conference Algoritmy,*, 81 - 90. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/1557/821
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Articles

## References

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[13] J. Valášek, P. Sváček, and J. Horáček, On suitable inlet boundary conditions for fluid-structure interaction problems in a channel, Applications of Mathematics 64:2 (2019), 225–251.

[14] W. Zhao, C. Zhang, S. H. Frankel, and L. Mongeau, Computational aeroacoustics of phonation, part I: Computational methods and sound generation mechanisms, The Journal of the Acoustical Society of America 112:5 (2002), 2134–2146.

[15] S. Zörner, M. Kaltenbacher, and M. Döllinger, Investigation of prescribed movement in fluid-structure interaction simulation for the human phonation process, Computers & Fluids 86 (2013), 133–140.

[2] M. Braack and P. B. Mucha, Directional do-nothing condition for the Navier-Stokes equations, Journal of Computational Mathematics 32 (2014), 507–521.

[3] M. Feistauer, P. Sváček, and J. Horáček, Numerical simulation of fluid-structure interaction problems with applications to flow in vocal folds, Fluid-structure Interaction and Biomedical Applications (T. Bodnár, G. P. Galdi, and S. Nečasová, eds.), Birkhauser, 2014, pp. 312–393.

[4] V. Girault and P. A. Raviart, Finite element methods for Navier-Stokes equations, Springer-Verlag, 1986.

[5] B. Kaltenbacher, M. Kaltenbacher, and I. Sim, A modified and stable version of a perfectly matched layer technique for the 3-D second order wave equation in time domain with an application to aeroacoustics, Journal of Computational Physics 235 (2013), 407–422.

[6] M. Kaltenbacher, Numerical simulation of mechatronic sensors and actuators: finite elements for computational multiphysics, Springer, 2015.

[7] M. A. Lodermeyer, A laser-based technique to evaluate sound generation during phonation, Ph.D. thesis, Friedrich-Alexander-Universität Erlangen-Nürnberg, 2019.

[8] W. S. Slaughter, Linearized elasticity problems, Springer, 2002.

[9] B. H. Story, I. R. Titze, and E. A. Hoffman, Vocal tract area functions from magnetic resonance imaging, The Journal of the Acoustical Society of America 100:1 (1996), 537–554.

[10] P. Sváček and J. Valášek, Mathematical modelling and numerical simulation of flow induced vibrations of vocal folds model with collisions, AIP Conference Proceedings, vol. 2116, AIP Publishing, 2019, p. 030003.

[11] I. R. Titze, Principles of voice production, Prentice Hall, 1994.

[12] J. Valášek, M. Kaltenbacher, and P. Sváček, On the application of acoustic analogies in the numerical simulation of human phonation process, Flow, Turbulence and Combustion (2018), 1–15.

[13] J. Valášek, P. Sváček, and J. Horáček, On suitable inlet boundary conditions for fluid-structure interaction problems in a channel, Applications of Mathematics 64:2 (2019), 225–251.

[14] W. Zhao, C. Zhang, S. H. Frankel, and L. Mongeau, Computational aeroacoustics of phonation, part I: Computational methods and sound generation mechanisms, The Journal of the Acoustical Society of America 112:5 (2002), 2134–2146.

[15] S. Zörner, M. Kaltenbacher, and M. Döllinger, Investigation of prescribed movement in fluid-structure interaction simulation for the human phonation process, Computers & Fluids 86 (2013), 133–140.