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

Pierre Carré, Joël Bensoam

Research output: Contribution to journalArticlepeer-review

Abstract

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.
Original languageEnglish
Article number117354
Pages (from-to)1-22
Number of pages22
JournalJournal of Sound and Vibration
Volume544
DOIs
Publication statusPublished - 3 Feb 2023

Keywords

  • Geometrically exact beam
  • Lagrangian mechanics
  • Lie group methods
  • Nonlinear string model
  • Sound synthesis

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