Experimental methods for characterization of one port nonlinear acoustic systems: application to sound absorbers
Résumé
Numerous sound absorbers dedicated to noise reduction at low frequencies are based on nonlinear properties (for example micro-perforated plates or nonlinear Helmholtz resonators). Classically (i.e. under linear assumption), the input impedance describes the behaviour of a sound absorber, considered as a one-port acoustic system, and measurement methods are available. Note that in tubes and in plane wave mode, the input impedance is defined for any cross-section of the tube as the ratio of the mean acoustic pressure to the volume velocity. It can be equivalently replaced by the reflection coefficient. The objective of this work is to develop identification techniques to characterize nonlinear elements at low frequencies, for increasing excitation levels. A specific setup of impedance tube named ''Short Kundt's Tube? was built able to reach very high sound levels at low frequencies. We used a swept-sine signal (also called chirp) exhibiting an exponential instantaneous frequency as excitation. We used only the resulting acoustic pressure measured inside the tube which is in front of the studied device. A calibration of the source had first to be done from measurements of known acoustic loads. Different approaches are discussed. The first one is defined as a linearisation method and gives access to the acoustic impedance quantities which are excitation level dependent. The second one is based on a nonlinear model able to characterize energy transfer to higher harmonics. It is defined as a scattering matrix linking the harmonic components of the input and output pressure wave amplitudes. These two approaches are defined in frequency domain. The third one is based on an Hammerstein model, and permits to obtain a nonlinear relation between the input and the output pressure wave, in time domain, without dependence on the excitation level. These techniques are applied for the study of different nonlinear vibroacoustic absorbers.
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