Weakly Nonlinear Gas Oscillations in Air-Filled Tubes; Solutions and Experiments

Ludovic Menguy (1) , Joël Gilbert (1)

1 LAUM - Laboratoire d'Acoustique de l'Université du Mans

The results of a theoretical and experimental investigation into the nonlinear, planar propagation of an acoustic signal in a cylindrical air-filled tube is presented. Assuming weakly nonlinear propagation and the distance of propagation smaller than the shock formation distance, the validity of the generalised Burgers' equation is analysed. The theoretical study is based on a dimensional analysis of the conservation equations followed by a calculation using asymptotic expansions. The deduced generalised Burgers' equations are solved whatever the boundary conditions are, with a numerical finite-difference method and using a harmonic balance method. Two cases are investigated experimentally: the purely progressive case, and the standing wave with an unknown termination. The results are compared successfully with theoretical predictions on the three first harmonics of a periodic signal in a high degree of accuracy, when the effects of the thermoviscous dissipation and of the non-linear propagation have the same order of magnitude.

Domaines: Acoustique [physics.class-ph]; Acoustique [physics.class-ph]

Ludovic Menguy, Joël Gilbert. Weakly Nonlinear Gas Oscillations in Air-Filled Tubes; Solutions and Experiments. Acta Acustica united with Acustica, 2000, 86 (5), pp.798-810. ⟨hal-00474991⟩