Abstract
This paper deals with flow induced vibrations of an elastic body. A simplified model of the human vocal fold is mathematically described. In order to consider the time dependent domain the arbitrary Lagrangian-Eulerian method is used. The viscous incompressible fluid flow and linear elasticity models are considered. The developed numerical schemes for the fluid flow and the elastic body are implemented by the in-house developed solver based on the finite element method. Preliminary numerical results testing the convergence of solver are presented.
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References
R.A. Adams, Sobolev Spaces (Academic, New York, 1975)
M. Braack, P.B. Mucha, Directional do-nothing condition for the Navier-Stokes equations. J. Comput. Math. 32, 507–521 (2014)
R. Clark, E.H. Dowell, A Modern Course in Aeroelasticity (Springer, 2004). http://www.springer.com/us/book/9781402027116
A. Curnier, Computational Methods in Solid Mechanics (Springer, Dordrecht/Boston, 1994)
T.A. Davis, Direct Methods for Sparse Linear Systems (SIAM, Philadelphia, 2006)
V. Girault, P.A. Raviart, Finite Element Methods for Navier-Stokes Equations (Springer, Berlin/New York, 1986)
R.C. Scherer, D. Shinwari, K.J. De Witt, C. Zhang, B.R. Kucinschi, A.A. Afjeh, Intraglottal pressure profiles for a symmetric and oblique glottis with a divergence angle of 10 degrees. J. Acoust. Soc. Am. 109, 1616–1630 (2001)
P. Sváček, J. Horáček, Numerical simulation of glottal flow in interaction with self oscillating vocal folds: comparison of finite element approximation with a simplified model. Commun. Comput. Phys. 12, 789–806 (2012)
N. Takashi, T.J.R. Hughes, An arbitrary Lagrangian-Eulerian finite element method for interaction of fluid and a rigid body. Comput. Methods Appl. Mech. Eng. 95, 115–138 (1992)
I.R. Titze, F. Alipour, The Myoelastic Aerodynamic Theory of Phonation (National Center for Voice and Speech, Denver/Iowa City, 2006)
J. Valášek, P. Sváček, J. Horáček, Numerical simulation of interaction of fluid flow and elastic structure modelling vocal fold. Appl. Mech. Mater. 821, 693–700 (2016)
S. Zörner, M. Kaltenbacher, M. Döllinger, Investigation of prescribed movement in fluid-structure interaction simulation for the human phonation process. Comput. Fluids 86, 133–140 (2013)
Acknowledgements
The financial support of this was partly provided by the Czech Science Foundation under the Grant No. P101/11/0207.
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Valášek, J., Sváček, P., Horáček, J. (2016). Numerical Approximation of Interaction of Fluid Flow and Elastic Structure Vibrations. In: Karasözen, B., Manguoğlu, M., Tezer-Sezgin, M., Göktepe, S., Uğur, Ö. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2015. Lecture Notes in Computational Science and Engineering, vol 112. Springer, Cham. https://doi.org/10.1007/978-3-319-39929-4_56
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DOI: https://doi.org/10.1007/978-3-319-39929-4_56
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