Sensitivity analysis of micro-perforated panel absorber models at high sound pressure levels Zacharie Laly a,⇑ , Noureddine Atalla a , Sid-Ali Meslioui b , Khalid El Bikri c a GAUS, Department of Mechanical Engineering, Université de Sherbrooke, Sherbrooke, Quebec J1K 2R1, Canada b Acoustics, Pratt & Whitney Canada, Longueuil, Quebec J4G 1A1, Canada c CM2SM, University Mohammed V of Rabat, Department of Mechanical Engineering, Rabat, Morocco article info Article history: Received 20 March 2019 Received in revised form 22 June 2019 Accepted 24 June 2019 Keywords: Sensitivity analysis Micro-perforated panel absorber Impedance model Higher pressure level Acoustic properties abstract Sensitivity analysis is performed using a nonlinear acoustic impedance model of micro-perforated panel absorbers constituted by a micro-perforated panel bonded on a honeycomb structure in order to assess the impacts of the input parameters on the outputs of interest namely the normalized surface impedance and the sound absorption coefficient. The theoretical results predicted by the nonlinear impedance model show good agreement with experimental measurements performed at high sound pressure level using an impedance tube. The inputs of the model are the plate thickness, the orifice diameter, the perforation ratio, the cavity depth and the sound pressure level. For higher pressure levels excitations, it is demon- strated that the perforation ratio is the key parameter which affects significantly the resistance and the sound absorption of the absorber at the resonance while the impacts of the thickness and orifice diameter of the panel are negligible. In addition, the study confirms that the acoustic reactance is dominated by the cavity depth especially at low frequencies and the sound pressure level influences strongly the acoustic behaviour of micro-perforated panel absorbers. Therefore, the design of a micro-perforated panel absor- ber requires the knowledge of the sound pressure level and the perforation ratio control quality must be done carefully in order to get the target performances of the absorber. Ó 2019 Elsevier Ltd. All rights reserved. 1. Introduction Noise reduction is an important topic in many industrial appli- cations and micro-perforated panels (MPP) are used for this pur- pose. MPP absorbers are applied on the internal walls of the turbofan engine nacelle both in the intake and by-pass ducts to reduce engine noise. Many theoretical and experimental studies were conducted in linear [3–6] and nonlinear regime [1,2,7–17] to characterize the acoustic properties of MPP which depend on the incident sound pressure level (SPL) on the surface of the perfo- rations. For low pressure levels, the acoustic energy is dissipated by viscous and thermal effects while at higher pressure levels, vor- tex and jet formation were observed at the exit of orifices [12,13]. Ingard and Ising [13] showed that the resistance of MPP at high SPL varies linearly with respect to the particle acoustic velocity in the perforation. The nonlinear phenomena induced by the high SPL affect the acoustic properties of MPP and dissipate acoustic energy that is converted into kinetic energy of the vortices [12]. It is there- fore interesting to investigate by a sensitivity analysis how the parameters of a MPP absorber affect its acoustic properties. An optimization of the design of MPP absorber or even its quality con- trol in the nonlinear regime requires understanding of the domi- nant parameters that control its acoustic performances. The aim is to investigate how the uncertainty in the output of a model of the MPP absorber can be apportioned to the uncertainty of the input parameters. A review of sampling-based methods for sensi- tivity analysis was done by Helton et al. [23]. Fey et al. [24] pre- sented a comparison of different sensitivity analysis methods which are used in various disciplines. They worked on identifica- tion and evaluation of sensitivity analysis methods in order to apply them to risk assessment models. The advantages and disad- vantages of some sensitivity analysis methods are illustrated in various works [25–27]. Ouisse et al. [18] investigated the sensitiv- ity analysis of porous material models using the equivalent fluid impedance model proposed by Champoux–Allard for a rigid frame porous material which contains five input parameters namely the porosity, the flow resistivity, the tortuosity and viscous and ther- mal characteristics lengths. They showed that the resistivity is the most influent parameter on the acoustic absorption and the surface impedance of porous material. Recently, Doutres et al. [19] used global sensitivity analysis to investigate the effect of https://doi.org/10.1016/j.apacoust.2019.06.025 0003-682X/Ó 2019 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: Zacharie.Laly@usherbrooke.ca (Z. Laly). Applied Acoustics 156 (2019) 7–20 Contents lists available at ScienceDirect Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust