Amplitude-dependent modal coefficients accounting for localized nonlinear losses in a time-domain integration of woodwind model

Abstract

This article develops the design of a sound synthesis model of a woodwind instrument by modal decomposition of the input impedance, taking into account viscothermal losses as well as localized nonlinear losses at the end of the resonator. This formalism has already been applied by Diab et al. [Journal of Sound and Vibration 528 (2022) 116892] to the study of forced systems. It is now implemented for self-oscillating systems. The employed method extends the definition of the input impedance to the nonlinear domain by adding a dependance on the RMS acoustic velocity at a geometric discontinuity. The poles and residues resulting from the modal decomposition are fitted as a function of this velocity. Thus, the pressure-flow relation defined by the resonator is completed by new equations which account for the dependence with the velocity at the end of the tube. To assess the ability of the model to reproduce a real phenomenon, comparisons with the experimental results of Atig et al. [PhD thesis, Université du Maine (2004)] and Dalmont and Frappé [Journal of the Acoustical Society of America 122(2) (2007) 1173–1179] were carried out. Simulations show that the model reproduces these experimental results qualitatively and quantitatively.