Acoustic performance of gratings of cylindrical voids in a soft elastic medium with a steel backing

Abstract

An approximate analytical model is presented to investigate sound transmission, reflection and absorption of a rubber-like medium comprising a single layer of periodic cylindrical voids attached to a steel backing. The layer of voids is modelled as a homogeneous medium with effective material and geometric properties. A numerical model based on the finite element method is developed to validate results from the homogenization model, as well as to show further insights into the physical mechanisms associated with the system acoustic performance. Monopole resonance of the voids is shown to reduce sound transmission through the voided medium due to increased reflection, resulting in poor sound absorption around this frequency. Peaks of high sound absorption are attributed to Fabry-Pérot resonance with the frequency of the first peak derivable by a lumped spring-mass analogy. Sound absorption for a single layer of voids in a soft elastic medium with a steel backing is shown to be similar to the sound absorption in the same elastic medium but without the steel backing, for a single layer of voids and its mirror image in the direction of sound propagation.

Theoretical requirements and inverse design for broadband perfect absorption of low-frequency waterborne sound by ultrathin metasurface

“…Then, a simple one-dimensional transfer matrix approach is used to calculate the acoustic performances under normal incidence. The transfer matrix of the (n−1)th layer, T n −1 , relates the output pressure and velocity to the input pressure and velocity by 50,53,65 where , l n −1 and are respectively the wave number, thickness and impedance of (n−1)th layer, with ρ n −1 and being the density and longitudinal wave speed of this layer. The full transfer matrix T for the multi-layer structure is obtained as the product of the individual transfer matrix for the layers.…”

“…Nevertheless, for the case the metasurfaces are bonded to the hull of an underwater vehicle, the hull vibration should not be neglected when the analysis is performed in low-frequency regime. Actually, it has been found by several researchers that the vibration of the steel plate of finite thickness has a significant effect on the acoustic absorptance of the rubbery coatings in low frequency range 46–50 . Therefore, it is more reasonable to treat the metasurface and the hull as a whole when the low-frequency acoustic performances are investigated.…”

Pochhammer-Chree Waves: Spectral Analysis of Axially Symmetric Modes

“…Substituting the displacement representation (23) into boundary conditions (26), yields the following equations written up to exponential multiplier …”

“…Extensions of the Pochhammer-Chree waves to helical waves (longitudinal axially symmetric modes) that relate to non-integer coefficients at the angle coordinate in the corresponding potentials were analyzed [24][25][26].…”

A Review of Tunable Acoustic Metamaterials

“…The manipulation of acoustic waves has been investigated intensively in last decades [90][91][92][93]. The development of AMMs provides a new platform for the manipulation of the propagation of acoustic waves, including the airborne acoustic wave [94][95][96], underwater acoustic wave [97][98][99][100], elastic wave [76,101,102], and surface acoustic wave [58]. The theoretical and experimental research of an acoustic cloak [103], acoustic rectification [53], acoustic lens [104,105], and near-zero index [106] have been carried out.…”