aUniversité de Lyon, Univ. Lyon 1, LMFA UMR CNRS 5509, F-69134 Ecully
bUniversité de Lyon, Ecole Centrale de Lyon, LMFA UMR CNRS 5509, F-69134 Ecully
Nonlinear propagation models for wave propagation in the resonator of brass instruments are generally based on a one-dimensional description. This description is made under the hypothesis that sound wave propagation does not depend on bends, and is the same for straight or curved resonators. However, brass instruments resonators are not straight, and the effects of bends have to be considered. Modal approaches have shown that the pressure field has no symmetry in curved ducts, both in linear and weakly nonlinear propagation. The present study addresses the question of the behavior of shockwaves in U-shaped tubes with geometries close to some parts of brass instruments resonators, For this purpose, both experiments and numerical simulations in time domain have been performed. The experiments are based on optical measurements requiring a square section of the U-shaped portion of the duct. The corresponding numerical simulations have been performed by solving the 2D Euler equations in curvilinear coordinates using a finite-difference time-domain approach. Results reveal the dynamics of shock propagation, the nonlinear interaction of shocks, and the distortion of the waveform.
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