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Modeling of the resonance of an acoustic wave in a torus. (English. French summary) Zbl 1282.35288

Summary: A pneumatic tyre in rotating motion with a constant angular velocity \(\Omega \) is assimilated to a torus whose generating circle has a radius \(R\). The contact of the tyre with the ground is schematized as an ellipse with semi-major axis \(a\). When \((\Omega R/C_{0})\ll 1\) and \((a/R)\ll 1\) (where \(C_{0}\) is the velocity of the sound), we show that at the rapid time scale \(R/C_{0}\), the air motion within a torus periodically excited on its surface generates an acoustic wave \(h\). A study of this acoustic wave is conducted and shows that the mode associated to \(p=0\) leads to resonance. In resonance the acoustic wave \(h\) moves quadratically in time and also decreases asymptotically faster when the mean pressure in the domain is low.

MSC:

35Q35 PDEs in connection with fluid mechanics
76Q05 Hydro- and aero-acoustics
35B10 Periodic solutions to PDEs
35B34 Resonance in context of PDEs
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References:

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