A Comparative Study between Experimental & Numerical Value of Subharmonic Acoustic Resonances

In a non linear system, a response at other then the driving frequency in often observed. We consider a closed tube in which the oscillations of a gas corum driven by the sinusoidal motion of a piston. For the investigated case (subharmonic resonances) the frequency of the piston displacement in the neighbourhood of half of the fundamental frequency. It can be show that near subharmonic resonances the acoustic theory breaks down for sufficiently small boundary?layer friction. The reason for this "breakdown" is that a second order nonlinear correction to the acoustic solution becomes resonant. we get a small boundary layer friction shocks are formed and the amplitude at subharmonic resonance is comparable with the nonresonant acoustic solution. Theoretical results are compared with the pressure signals measured at the closed end of a resonance tube. These fundamental experiments show the existence of a subharmonic resonance with shocks predicted by the nonlinear theory bv. J.J. Keller (1975) and consequently the breakdown of the acoustic solution in a case for which the acoustic solution does not become singular.