Two-dimensional motion of a viscoelastic membrane in an incompressible fluid: Applications to the cochlear mechanics

Y. N. Domínguez-del Ángel; M. Núñez-López; J. G. González-Santos; A. López-Villa

doi:10.1007/978-3-319-27965-7_18

Two-dimensional motion of a viscoelastic membrane in an incompressible fluid: Applications to the cochlear mechanics

Y. N. Domínguez-del Ángel, M. Núñez-López, J. G. González-Santos, A. López-Villa

Escuela Superior de Ingeniería Mecánica y Eléctrica (ESIME), Unidad Azcapotzalco

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this work we present the two-dimensional motion of a viscoelastic membrane immersed in incompressible inviscid and viscous fluids. The motion of the fluid is modelled by two-dimensional Navier-Stokes equations, and a constitutive equation is considered for the membrane which captures along with the fluid equations the essential features of the vibrations of the fluid. By using the Fourier transform, the linearized equations are reduced to a functional equation for membrane displacement which is solved analytically and the inverse transform is evaluated asymptotically. Results obtained show some of the basic known characteristics of cochlear mechanics.

Original language	English
Title of host publication	Recent Advances in Fluid Dynamics with Environmental Applications
Editors	Leonardo Di G. Sigalotti, Abraham Medina, Abel López, Jaime Klapp, Gerardo Ruiz-Chavarría
Publisher	Kluwer Academic Publishers
Pages	229-252
Number of pages	24
ISBN (Print)	9783319279640
DOIs	https://doi.org/10.1007/978-3-319-27965-7_18
State	Published - 2016
Event	1st Conference on Spring School Enzo Levi, 2014 - Mexico, Mexico Duration: 12 May 2014 → 13 May 2014

Publication series

Name	Environmental Science and Engineering (Subseries: Environmental Science)
ISSN (Print)	1863-5520

Conference

Conference	1st Conference on Spring School Enzo Levi, 2014
Country/Territory	Mexico
City	Mexico
Period	12/05/14 → 13/05/14

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10.1007/978-3-319-27965-7_18

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Domínguez-del Ángel, Y. N., Núñez-López, M., González-Santos, J. G., & López-Villa, A. (2016). Two-dimensional motion of a viscoelastic membrane in an incompressible fluid: Applications to the cochlear mechanics. In L. D. G. Sigalotti, A. Medina, A. López, J. Klapp, & G. Ruiz-Chavarría (Eds.), Recent Advances in Fluid Dynamics with Environmental Applications (pp. 229-252). (Environmental Science and Engineering (Subseries: Environmental Science)). Kluwer Academic Publishers. https://doi.org/10.1007/978-3-319-27965-7_18

Domínguez-del Ángel, Y. N. ; Núñez-López, M. ; González-Santos, J. G. et al. / Two-dimensional motion of a viscoelastic membrane in an incompressible fluid : Applications to the cochlear mechanics. Recent Advances in Fluid Dynamics with Environmental Applications. editor / Leonardo Di G. Sigalotti ; Abraham Medina ; Abel López ; Jaime Klapp ; Gerardo Ruiz-Chavarría. Kluwer Academic Publishers, 2016. pp. 229-252 (Environmental Science and Engineering (Subseries: Environmental Science)).

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abstract = "In this work we present the two-dimensional motion of a viscoelastic membrane immersed in incompressible inviscid and viscous fluids. The motion of the fluid is modelled by two-dimensional Navier-Stokes equations, and a constitutive equation is considered for the membrane which captures along with the fluid equations the essential features of the vibrations of the fluid. By using the Fourier transform, the linearized equations are reduced to a functional equation for membrane displacement which is solved analytically and the inverse transform is evaluated asymptotically. Results obtained show some of the basic known characteristics of cochlear mechanics.",

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Domínguez-del Ángel, YN, Núñez-López, M, González-Santos, JG & López-Villa, A 2016, Two-dimensional motion of a viscoelastic membrane in an incompressible fluid: Applications to the cochlear mechanics. in LDG Sigalotti, A Medina, A López, J Klapp & G Ruiz-Chavarría (eds), Recent Advances in Fluid Dynamics with Environmental Applications. Environmental Science and Engineering (Subseries: Environmental Science), Kluwer Academic Publishers, pp. 229-252, 1st Conference on Spring School Enzo Levi, 2014, Mexico, Mexico, 12/05/14. https://doi.org/10.1007/978-3-319-27965-7_18

Two-dimensional motion of a viscoelastic membrane in an incompressible fluid: Applications to the cochlear mechanics. / Domínguez-del Ángel, Y. N.; Núñez-López, M.; González-Santos, J. G. et al.
Recent Advances in Fluid Dynamics with Environmental Applications. ed. / Leonardo Di G. Sigalotti; Abraham Medina; Abel López; Jaime Klapp; Gerardo Ruiz-Chavarría. Kluwer Academic Publishers, 2016. p. 229-252 (Environmental Science and Engineering (Subseries: Environmental Science)).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - Two-dimensional motion of a viscoelastic membrane in an incompressible fluid

T2 - 1st Conference on Spring School Enzo Levi, 2014

AU - Domínguez-del Ángel, Y. N.

AU - Núñez-López, M.

AU - González-Santos, J. G.

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N1 - Publisher Copyright: © Springer International Publishing Switzerland 2016.

PY - 2016

Y1 - 2016

N2 - In this work we present the two-dimensional motion of a viscoelastic membrane immersed in incompressible inviscid and viscous fluids. The motion of the fluid is modelled by two-dimensional Navier-Stokes equations, and a constitutive equation is considered for the membrane which captures along with the fluid equations the essential features of the vibrations of the fluid. By using the Fourier transform, the linearized equations are reduced to a functional equation for membrane displacement which is solved analytically and the inverse transform is evaluated asymptotically. Results obtained show some of the basic known characteristics of cochlear mechanics.

AB - In this work we present the two-dimensional motion of a viscoelastic membrane immersed in incompressible inviscid and viscous fluids. The motion of the fluid is modelled by two-dimensional Navier-Stokes equations, and a constitutive equation is considered for the membrane which captures along with the fluid equations the essential features of the vibrations of the fluid. By using the Fourier transform, the linearized equations are reduced to a functional equation for membrane displacement which is solved analytically and the inverse transform is evaluated asymptotically. Results obtained show some of the basic known characteristics of cochlear mechanics.

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BT - Recent Advances in Fluid Dynamics with Environmental Applications

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Domínguez-del Ángel YN, Núñez-López M, González-Santos JG, López-Villa A. Two-dimensional motion of a viscoelastic membrane in an incompressible fluid: Applications to the cochlear mechanics. In Sigalotti LDG, Medina A, López A, Klapp J, Ruiz-Chavarría G, editors, Recent Advances in Fluid Dynamics with Environmental Applications. Kluwer Academic Publishers. 2016. p. 229-252. (Environmental Science and Engineering (Subseries: Environmental Science)). doi: 10.1007/978-3-319-27965-7_18

Two-dimensional motion of a viscoelastic membrane in an incompressible fluid: Applications to the cochlear mechanics

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