Sound absorption by rubber coatings with periodic voids and hard inclusions Gyani Shankar Sharma a,⇑ , Alex Skvortsov b , Ian MacGillivray b , Nicole Kessissoglou a a School of Mechanical and Manufacturing Engineering, The University of New South Wales, Sydney 2052, Australia b Maritime Division, Defence Science and Technology, Melbourne 3207, Australia article info Article history: Received 22 May 2018 Received in revised form 2 August 2018 Accepted 6 September 2018 Keywords: Acoustic coating Phononic crystals Soft elastic material Effective medium approximation Finite element method abstract Sound absorption by viscoelastic coatings for underwater applications comprising both periodically dis- tributed voids and hard inclusions is presented. Using effective medium theory, each layer of gratings is approximated as a homogeneous medium with effective material and geometric properties, in which the monopole and dipole resonances of the inclusions are taken into account. A finite element model of the periodically distributed voided and hard inclusions in the host rubber medium is also developed. The dif- ferent combinations of the layers are shown to have markedly different impacts on the acoustic perfor- mance, whereby the physical mechanisms governing sound absorption are strongly dependent on the Fabry-Pérot and dipole resonances associated with the presence of the inclusions. The effects of water backing or a steel backing plate are also shown to significantly affect the acoustic performance for the different layers of inclusions. Ó 2018 Elsevier Ltd. All rights reserved. 1. Introduction Locally resonant phononic crystals are composite structures comprising sound scatterers in elastic media. Two main mecha- nisms governing the acoustic performance of phononic crystals are local resonance of the scatterers and destructive wave interfer- ence attributed to Bragg scattering due to periodicity of the scat- terers [1,2]. For homogeneous materials, the density and elastic moduli are positive, whereas for materials with inclusions, the occurrence of local resonances lead to effective density or elastic moduli which are frequency dependent and can be zero or negative at some frequencies [3–8]. Resonant responses of the effective den- sity and elastic moduli can be simultaneously achieved using pho- nonic crystals that exhibit monopole, dipole and quadrupole resonances [8–11]. Utilising these phenomena, phononic crystals can be engineered to control air-borne or water-borne sound waves [3–5,12–15]. Inspired by phononic crystals with simultaneous resonant den- sity and elastic moduli, the motivation of the current work is to investigate simple designs of phononic crystals for use as acoustic coatings that can be externally applied to marine vessels. These coatings play a dual role to minimise underwater noise pollution and absorb external acoustic waves for stealth purposes. To avoid reflection of sound waves, soft elastic media such as rubber with impedances close to the impedance of water are used. Further, soft elastic media embedded with inclusions facilitate the conversion of longitudinal waves into shear waves by inducing local resonances, thereby increasing sound dissipation. Acoustic coatings were ini- tially designed using soft rubber containing periodic cavities [16,17], and later with heavy metallic inclusions [18]. A coating comprising heavy inclusions can be used in a deep sea environ- ment as its sound absorption performance is less sensitive to the ambient fluid pressure compared to a coating comprising voids [19]. On the other hand, a coating comprising voids is lighter in weight compared to a coating comprising heavy inclusions. Further, compared to a coating comprising hard inclusions, a coat- ing with voids is more efficient in blocking the transmission of noise from marine vessels [19–21]. A large number of analytical [16–18,21–26], numerical [24–41] and experimental [17,21,22,33–35] studies have been conducted to study the acous- tic performance of coatings. Coatings with inclusions of different shapes such as cylindrical scatterers [16,17,24–27,35–38] and spherical scatterers [18,21–23,27–30], as well as different materi- als such as voided scatterers [16,17,21–25,27–31,35–40] and hard scatterers [18,26,28,32–34,39] have also been investigated. To the best of the authors’ knowledge, none of the aforemen- tioned studies have considered the simultaneous inclusion of grat- ings comprising voided and hard scatterers, and their combined effect on sound absorption of an underwater acoustic coating. This https://doi.org/10.1016/j.apacoust.2018.09.003 0003-682X/Ó 2018 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: gyanishankar.sharma@unsw.edu.au (G.S. Sharma). Applied Acoustics 143 (2019) 200–210 Contents lists available at ScienceDirect Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust