Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Broadband acoustic absorption by phononic crystal comprising multi-periodic hard and void cylinders
Mingsheng Wang, Haoqi Hao, Qiang Liu*
*Corresponding Author
Hangzhou Applied Acoustic Research Institude
Hangzhou, Zhejiang, China
is much larger than acoustic impedance in air, so that hard inclusion(steel) in air has to be considered as elastic material in water. These two
disadvantages result in great limitation on the study of underwater
acoustic absorption.

ABSTRACTThe underwater acoustical model structured by two steel cylinders anda void cylinder embedded in rubber medium with steel and air backing
or water backing is proposed in this paper, based on the theory of soundresonance absorption. Through the commercial software Comsol 5.4,
the underwater absorption coefficient and displacement deformation ofphononic crystal are performed. Then, sound absorption coefficient ofphononic crystal with steel and air backing or with water backing isplotted, which provides a perfect idea to re-construct anechoic tile. The
numerical results show that the underwater sound absorption frequency
band could be broadened by utilizing coupled multi-resonator modes
between steel cylinder and void. In addition, results reveal that massspring resonant mode has significant impacts at low-frequency
absorption and the conversation from longitudinal waves to the shear
waves is inspected at mid-frequency band through observation of
displacement deformation of phononic crystal. This paper can offer apractical guidance to design and construct phononic crystal which iscomprised by multi-periodic steel and void cylinders.

Recently, investigations on underwater acoustic absorption by
pentamode material (Milton, 1995), acoustic resonances (Wen, 2011),
and gradient acoustic material (Naify, 2014) have attracted increasing
interest. As introduced in paper (Zhao, 2010), viscoelastic polymer
slabs designed with locally resonant scatters (heavy spheres coated bysoft silicon rubber) in water enhance low-frequency absorption
significantly. In addition, underwater acoustic absorption of backing
inclusion for localized resonant scatters is further investigated and thethickness and mass affect acoustic absorption efficiency and frequency
range obviously (Zhao, 2014). Due to narrow frequency range with asingly periodic array of cylindrical scatters, broadening the absorption
band by using anechoic layers with scatters of mixed size is feasible
method significantly (Yang, 2014). By using monopole resonances ofvoids and dipole resonances of hard inclusion for viscoelastic coating,working frequency of underwater acoustic absorption is broadened insome degree (Sharma, 2019). By using a structure for an underwatersound absorber with subwavelength thickness, not only can soundwaves be slowed in coating, but also multiple local bending modes andlocal longitudinal modes could also be stimulated, resulting in quasiperfect absorption for multiple frequencies (Zhang, 2018). Through thefunctionally graded materials (FGM) using a method of the finite
element (FEM) and boundary element (BEM), not only the weight oflaying submarine section but also the sound radiation power are both
reduced (Zhang, 2013). Using expanded polystyrene (EPS) foams
filling chiral covering layers, the underwater sound radiation of floating
structures is decreased (Zhu, 2015).

KEY WORDS: Phononic crystals, Finite element method, Massapring resonance

INTRODUCTION
In recent years, there has been growing interests in the acoustic
strength of underwater vehicle for many researchers. Various kinds ofphononic crystals are designed and applied to the anechoic coating ofsubmarines to reduce the reflection and increase the absorption ofsound wave emitted from the active sonar, and anechoic coatingconstructed by phononic crystals could also modify the acoustic
strength performance of underwater vehicles. In addition, increased
attention has been focused on the study of acoustic absorption by using
dark acoustic metamaterials (Mei, 2012), coiling up space (Li, 2012),
active sound control (Kundu, 2011), gradient acoustic metasurface(Yuan, 2015). Besides, sonic crystals made from localized resonant
structures perform spectral gaps with two orders of magnitude smaller
than the relevant wavelength (Liu, 2000). However, theseinvestigations are mainly focused on air sound absorption, and researchand experiment about underwater acoustic absorption receive lessattention additionally. In fact, acoustic wavelength in air is much lessthan 5 times compared with underwater acoustic wavelength for thesame sound frequency. On the other hand, acoustic impedance in water

In this paper, we investigate the acoustic absorption performance ofelastic medium embedded with layers of periodically distributed voids
and metallic inclusions about low-frequency broadband absorption
numerically. Based on the results of different combinations of voidsand metallic inclusions with steel and air back inclusion or waterbacking, it is clearly shown that the order of each layer of gratings in
the direction of sound propagation has a perfect benefit on low and mid
frequency acoustical absorption in water.

MODEL AND CALCULATION METHOD

1002