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This article develops the design of a sound synthesis model of a woodwindinstrument by modal decomposition of the input impedance, taking into accountviscothermal losses as well as localized nonlinear losses at the end of theresonator. This formalism has already been applied by Diab et al. (2022) to thestudy of forced systems. It is now implemented for self-oscillating systems.The employed method extends the denition of the input impedance to thenonlinear domain by adding a dependance on the RMS acoustic velocity at ageometric discontinuity. The poles and residuals resulting from the modaldecomposition are interpolated as a function of this velocity. Thus, thepressure-ow relation dened by the resonator is completed by new equations whichaccount for the dependence with the velocity at the end of the tube. To assessthe ability of the model to reproduce a real phenomenon, comparisons with theexperimental results of Atig et al. (2004) and Dalmont et al. (2007) werecarried out. Simulations show that the model reproduces these experimentalresults qualitatively and quantitatively.

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