Nonlinear plate vibrations: A modal approach with application to cymbals and gongs

Cyril Touze; Michele Duccheschi; Stefan Bilbao

Nonlinear plate vibrations: A modal approach with application to cymbals and gongs

Cyril Touze, Michele Duccheschi, Stefan Bilbao

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

Abstract

A von Karm´ an simply supported plate is considered. A general strategy is developed for the solution of the nonlin- ´
ear equations: the solution is expanded onto the linear normal modes for the displacement and stress function. To
this extent, a general numerical method is devised to deal with cases where no analytical solutions are available.
Description of the nonlinear coupling coefficients can then be done in terms of the linear eigenfunctions. The role
of these coefficients is shown to be involved in explaining the complicated dynamics of the plate in nonlinear free
oscillations. The current model is validated through comparison with other results in the literature and thanks to a
finite difference scheme.

Original language	English
Title of host publication	Proceedings of the Joint Meeting of the Société Française d'Acoustique and the Institute of Acoustics
Number of pages	6
Publication status	Published - 2012
Event	Acoustics 12 - Nantes, France Duration: 23 Apr 2012 → 27 Apr 2012

Conference

Conference	Acoustics 12
Country/Territory	France
City	Nantes
Period	23/04/12 → 27/04/12

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Acoustics2012_Ducceschi
© Touze, C., Duccheschi, M., & Bilbao, S. (2012). Nonlinear plate vibrations: A modal approach with application to cymbals and gongs. In Proceedings of the Joint Meeting of the Société Française d'Acoustique and the Institute of Acoustics.
Final published version, 511 KB

http://perso.ensta-paristech.fr/~touze/PDF/Acoustics2012_Ducceschi.pdf

Cite this

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title = "Nonlinear plate vibrations: A modal approach with application to cymbals and gongs",

abstract = "A von Karm´ an simply supported plate is considered. A general strategy is developed for the solution of the nonlin- ´ ear equations: the solution is expanded onto the linear normal modes for the displacement and stress function. To this extent, a general numerical method is devised to deal with cases where no analytical solutions are available. Description of the nonlinear coupling coefficients can then be done in terms of the linear eigenfunctions. The role of these coefficients is shown to be involved in explaining the complicated dynamics of the plate in nonlinear free oscillations. The current model is validated through comparison with other results in the literature and thanks to a finite difference scheme.",

author = "Cyril Touze and Michele Duccheschi and Stefan Bilbao",

year = "2012",

language = "English",

booktitle = "Proceedings of the Joint Meeting of the Soci{\'e}t{\'e} Fran{\c c}aise d'Acoustique and the Institute of Acoustics",

note = "Acoustics 12 ; Conference date: 23-04-2012 Through 27-04-2012",

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TY - GEN

T1 - Nonlinear plate vibrations: A modal approach with application to cymbals and gongs

AU - Touze, Cyril

AU - Duccheschi, Michele

AU - Bilbao, Stefan

PY - 2012

Y1 - 2012

N2 - A von Karm´ an simply supported plate is considered. A general strategy is developed for the solution of the nonlin- ´ ear equations: the solution is expanded onto the linear normal modes for the displacement and stress function. To this extent, a general numerical method is devised to deal with cases where no analytical solutions are available. Description of the nonlinear coupling coefficients can then be done in terms of the linear eigenfunctions. The role of these coefficients is shown to be involved in explaining the complicated dynamics of the plate in nonlinear free oscillations. The current model is validated through comparison with other results in the literature and thanks to a finite difference scheme.

AB - A von Karm´ an simply supported plate is considered. A general strategy is developed for the solution of the nonlin- ´ ear equations: the solution is expanded onto the linear normal modes for the displacement and stress function. To this extent, a general numerical method is devised to deal with cases where no analytical solutions are available. Description of the nonlinear coupling coefficients can then be done in terms of the linear eigenfunctions. The role of these coefficients is shown to be involved in explaining the complicated dynamics of the plate in nonlinear free oscillations. The current model is validated through comparison with other results in the literature and thanks to a finite difference scheme.

M3 - Conference contribution

BT - Proceedings of the Joint Meeting of the Société Française d'Acoustique and the Institute of Acoustics

T2 - Acoustics 12

Y2 - 23 April 2012 through 27 April 2012

ER -

Nonlinear plate vibrations: A modal approach with application to cymbals and gongs

Abstract

Conference

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