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

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.