Sound synthesis of a 3D nonlinear string using a covariant Lie group integrator of a geometrically exact beam model

We present a three dimensional nonlinear string model based on a geometrically exact beam. The beam model is obtained by applying a variational principle using a covariant Lagrangian formulation; in particular, the equations of motion and the boundary conditions are treated in an unified manner. Fol...

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Bibliographic Details
Published in:Journal of sound and vibration 2023-02, Vol.544, p.117354, Article 117354
Main Authors: Carré, Pierre, Bensoam, Joël
Format: Article
Language:English
Subjects:
Acoustics
Geometrically exact beam
Lagrangian mechanics
Lie group methods
Mechanics
Nonlinear string model
Physics
Sound synthesis
Vibrations
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Summary:We present a three dimensional nonlinear string model based on a geometrically exact beam. The beam model is obtained by applying a variational principle using a covariant Lagrangian formulation; in particular, the equations of motion and the boundary conditions are treated in an unified manner. Following an analogous discrete variational principle, a Lie group variational integrator is given. The energy and momentum conservation properties of the integrator are discussed and illustrated. This geometrically exact beam serves as a basis to formulate a prestressed damped string model with coupled non trivial boundary conditions. Simulation results are discussed and validated against analytical solutions obtained in the context of a small displacement hypothesis.
ISSN:0022-460X
1095-8568
DOI:10.1016/j.jsv.2022.117354