Development of 3D boundary element method for the simulation of acoustic metamaterials/metasurfaces in mean flow for aerospace applications

Abstract

Low-cost airlines have significantly increased air transport, thus an increase in aviation noise. Therefore, predicting aircraft noise is an important component for designing an aircraft to reduce its impact on environmental noise along with the cost of testing and certification. The aim of this work is to develop a three-dimensional Boundary Element Method (BEM), which can predict the sound propagation and scattering over metamaterials and metasurfaces in mean flow. A methodology for the implementation of metamaterials and metasurfaces in BEM as an impedance patch is presented here. A three-dimensional BEM named as BEM3D has been developed to solve the aero-acoustics problems, which incorporates the Fast Multipole Method to solve large scale acoustics problems, Taylor’s transformation to account for uniform and non-uniform mean flow, impedance and non-local boundary conditions for the implementation of metamaterials. To validate BEM3D, the predictions have been benchmarked against the Finite Element Method (FEM) simulations and experimental data. It has been concluded that for no flow case BEM3D gives identical acoustics potential values against benchmarked FEM (COMSOL) predictions. For Mach number of 0.1, the BEM3D and FEM (COMSOL) predictions show small differences. The difference between BEM3D and FEM (COMSOL) predictions increases further for higher Mach number of 0.2 and 0.3. The increase in difference with Mach number is because Taylor’s Transformation gives an approximate solution for the boundary integral equation. Nevertheless, it has been concluded that Taylor’s transformation gives reasonable predictions for low Mach number of up to 0.3. BEM3D predictions have been validated against experimental data on a flat plate and a duct. Very good agreement has been found between the measured data and BEM3D predictions for sound propagation without and with the mean flow at low Mach number.

Programmable 3D metamaterials with tailored Poisson's ratios over large deformation

“…We use Newton's method to solve (2) with a standard Armijo backtracking algorithm to determine the step size in each iteration. The detailed formulations of the gradient and Hessian matrix are provided in Supplementary Equations (12,25).…”

“…While there are 2D or pseudo-3D metamaterials possessing these properties 8,9 , this paper advocates for 3D metamaterials to mitigate the limitation and enhance their efficacy and applicability in real-world scenarios 10 . The ability to tailor these fundamental properties enhances the adaptability and reliability of 3D metamaterials, paving the way for transformative advancements in materials science and engineering 11 , aerospace 12 , robotics 13 , and beyond.…”

Fast topology optimization of phononic crystal‐based metastructures for vibration isolation by deep learning

“…Metastructures are getting more and more attention in various fields, such as aerospace, mechanical, and civil engineering (Bashir & Carley, 2020;T. Li et al, 2020;Oseev et al, 2013;Ouakka et al, 2023).…”

“…Metastructures are getting more and more attention in various fields, such as aerospace, mechanical, and civil engineering (Bashir & Carley, 2020; T. Li et al., 2020; Oseev et al., 2013; Ouakka et al., 2023). They hold particular significance in the area of vibration isolation and reduction, which is a crucial concern in civil engineering (Gutierrez Soto & Adeli, 2018, 2019; Javadinasab Hormozabad et al., 2021; Kim & Adeli, 2005; Z. Li & Adeli, 2018).…”

A simple mass oscillator metasurface design with linear phase shift

“…In the past decade, metamaterials have been widely studied by many scholars because they can realize the extraordinary physical properties that are not found in nature. Their unique physical properties have been widely applied in many fields, such as electromagnetic field [1,2], and acoustic/elastic wavefield [3][4][5], etc. However, the complex three-dimensional structure and periodic arrangement requirements of metamaterials will lead to their disadvantages such as bulk volume and difficult preparation.…”