# A Perforated Plate with Stepwise Apertures for Low Frequency Sound Absorption
###### Abstract  
A perforated plate with stepwise apertures (PPSA) is proposed to improve sound absorption for low frequencies. In contrast with an ordinary perforated plate with insufficient acoustic resistance and small acoustic mass, the perforated plate with stepped holes could match the acoustic resistance of air characteristic impedance and also moderately increase acoustic mass especially at low frequencies. Prototypes made by 3D printing technology are tested in an impedance tube. The measured results agree well with that of prediction through theoretical and numerical models. In addition, an absorber array of perforated plates with stepwise apertures is presented to  
mainly depends on the part of small holes, and the part of large holes is only to increase the plate thickness. [PERSON] et al. [11] experimentally analyzed the effects of tapered and stepped holes on the sound absorption performance of thick MPP, and the results showed that large tapered holes can broaden the absorption bandwidth in the higher frequency domain. Based on the MPP model, [PERSON] [12] performed an equivalent simulation of the experimental results for a tapered MPP, and the equivalent aperture obtained is between the large part and the small part of the tapered hole. [PERSON] et al. [13] developed a numerical model of MPP with a tapered hole in the acoustic module of COMSOL Multiphysics, and the simulation results showed that the absorption performance of MPP with tapered holes was mainly influenced by the inlet diameter and outlet diameter. In addition, [PERSON] et al. [14] gave an empirical impedance correction model related to the cross-sectional ratio based on 176 sets of numerical simulations. These aforementioned literatures concern with reducing the excess acoustic resistance of large-thick MPPs by replacing straight-through holes with sub-millimeter variable cross-section holes. In comparison with MPP, perforated plates with large apertures have the advantage of less perforation holes if the acoustic resistance can be improved sufficiently through some ways. Recently, various perforated structures for low to medium sound absorption, such as perforated panel with extended tubes (PPET) [15], composite honeycomb sandwich panels (CHSPs) [16], perforated composite Helmholtz-resonator (PCHR) [17], coiled space resonators (CSRs) [18], parallel-arranged perforated panel absorbers (PPAs) [19], panel containing coiled Helmholtz resonators [20] and inhomogeneous multi-layer Helmholtz resonators with extended necks (HRENs) [21], have been investigated. However, perforated plates with stepwise apertures for low frequency sound absorption have not been reported. For this motivation, a perforated plate with stepwise apertures (PPSA) larger than 1.5 mm is proposed for low-frequency (100-300 Hz) sound absorption in a compact space. Additionally, the array structures consisting of multiple sub-absorbers in parallel arrangement have been studied to improve the sound absorption. [PERSON] et al. [22] designed a MPP absorber array with two different cavities and gave the measured normal absorption coefficients by impedance tube. [PERSON] et al. [23] established a numerical model to study the sound absorption mechanism of a MPP absorbers array with different cavity depths in detail. [PERSON] et al. [24; 25] studied a permeable membranes absorber array (PMAR) numerically and experimentally, and the results showed that PMAR is an effective absorbing structure due to the influence of multiple locally reacting air cavities at different depths. Furthermore, [PERSON] et al. [26] proposed a profiled structure using perforated plates in some wells, thus adjusting the depths of the wells to improve low frequency absorption. In this paper, based on the local resonance effect, without changing the structure parameters, a simple PPSA absorbers array is initially designed to extend the sound absorption bandwidth only by inserting one rigid partition plate in the air cavity. This paper is organized as follows.