Diffusive representations for the analysis and simulation of flared acoustic pipes with visco-thermal losses

Thomas Hélie (1, 2) , Denis Matignon (3)

1 STMS - Sciences et Technologies de la Musique et du Son
2 Analyse et synthèse sonores [Paris]
3 TSI - Département Traitement du Signal et des Images

Acoustic waves travelling in axisymmetric pipes with visco-thermal losses at the wall obey a Webster–Lokshin model. Their simulation may be achieved by concatenating scattering matrices of elementary transfer functions associated with nearly constant parameters (e.g. curvature). These functions are computed analytically and involve diffusive pseudo-differential operators, for which we have representation formula and input-output realizations, yielding direct numerical approximations of finite order. The method is based on some involved complex analysis.

Mots clés: Wave propagation; Pseudo-differential operators; Complex analysis of multi-valued functions; Diffusive representations

Domaines: Modélisation et simulation; Musique, musicologie et arts de la scène; Neurosciences; Acoustique [physics.class-ph]; Traitement du signal et de l'image [eess.SP]

Thomas Hélie, Denis Matignon. Diffusive representations for the analysis and simulation of flared acoustic pipes with visco-thermal losses. Mathematical Models and Methods in Applied Sciences, 2006, 16 (4), pp.503-536. ⟨10.1142/S0218202506001248⟩. ⟨hal-01373407⟩