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2024 | OriginalPaper | Chapter

4. Exploiting the Use of Strong Nonlinearity in Dynamics and Acoustics: The Case of Musical Wind Instruments

Authors : Bruno Cochelin, Vincent Fréour, Christophe Vergez

Published in: Exploiting the Use of Strong Nonlinearity in Dynamics and Acoustics

Publisher: Springer Nature Switzerland

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Abstract

In this note, a physical model of the trumpet musical instrument is presented as a perfect example of a dynamical system where a strong nonlinearity is mandatory to produce the desired behaviour. After a description of the resonator model, ie, the air-column inside the trumpet, a strongly nonlinear one dof model is presented for modeling the lips of the player and the input flow. The bifurcation diagram with a control parameter being the player’s mouth pressure is then described in detail. The last section is devoted to the “in-house” MANLAB toolbox that has been used to follow the periodic solution branches of this trumpet model. It combines a high order harmonic balance method (Fourier series) with a high order Taylor series continuation, the so-called Asymptotic Numerical Method. An efficient computation is achived by first recasting the original strongly nonlinear system into an extended one with a polynomial quadratic nonlinearity only.

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previous chapter Tailoring Nonlinear Normal Modes and Managing Bifurcations

next chapter Global Nonlinear Dynamics: Challenges in the Analysis and Safety of Deterministic or Stochastic Systems

This pressure being computed from the modal shape as \(p_p^{(k)}(x)= - \rho _0 \dot{\phi _p}^{(k)}(x)\)

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Title: Exploiting the Use of Strong Nonlinearity in Dynamics and Acoustics: The Case of Musical Wind Instruments
Authors: Bruno Cochelin
Vincent Fréour
Christophe Vergez
Publisher: Springer Nature Switzerland
Book: Exploiting the Use of Strong Nonlinearity in Dynamics and Acoustics
Print ISBN: 978-3-031-56901-2

Electronic ISBN: 978-3-031-56902-9

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-3-031-56902-9_4