Elsevier

Applied Acoustics

Volume 164, July 2020, 107253
Applied Acoustics

Efficient numerical evaluation of transmission loss in homogenized acoustic metamaterials for aeronautical application

https://doi.org/10.1016/j.apacoust.2020.107253Get rights and content

Abstract

This work wants to investigate the soundproofing level of passive acoustic metamaterials made of Melamine Foam and cylindrical Aluminum inclusions. Latest research shows promising acoustical possibilities on controlling certain frequencies, varying their geometry or material configuration. Typically, acoustic metamaterials are plates with inclusions that resonate in low frequencies and block basses. Investigation is carried to use them for the improvement of aircraft cabin quietness. An homogenization method is adopted to study the metamaterial: this is modelled as viscoelastic material with inclusions, using a frequency-dependent approach, and the effective properties of the homogenized metamaterial are derived using a micromechanics-based method that allow us to prescribe the simplest mesh for periodical geometries (in this case, cylindrical) by reducing drastically the computation time. MSC Actran is used for vibro-acoustic simulations, in particular for the evaluation of Sound Transmission Loss in metamaterial panels with different volume fractions and in a sandwich panel with metamaterial core. This last has been compared with a classical sandwich panel used in aeronautics and it has been demonstrated that metamaterial gets higher transmission loss over all the frequency range.

Introduction

This paper aims to investigate innovative materials, namely metamaterials, suitable for the fuselage of aircraft in order to reduce the problem of noise and vibrations in the cabin [1], [2]. Aeronautical regulations, like FAR and EASA, mainly dictate safety standards, although a part of them is also devoted to environmental noise aspects [3]. Hence, interior noise requirements in civil aviation mainly derive from airline requests [4], which are based on passengers and cabin crew subjective response [5]. Since new products are always expected to have improved technical characteristics in order to compete on the market, the noise problem is nowadays attacking also small aircraft with classical configurations because of their lower technological level compared to big airplanes and the stringency of the aeronautical rules which become with the time more sensitive to noise aspects [6], [7].

Acoustic treatments, that are all the technical solutions installed on board to increase the noise reduction through the fuselage wall or to control the internal noise sources, have a fundamental importance to define the internal noise requirements [8]. Some technologies proposed in the past are resumed in the work by Dobrzynski [9]: thermo-acoustic blankets, skin damping, furnishing panels, mufflers and active noise control systems may be regarded as noise treatments. These need to be optimized taking into account different parameters, particularly the weight, the footprint and the cost; an example is given by the honeycomb acoustic metamaterial proposed by Sui et al. [10], which possesses lightweight and yet sound-proof properties. For these reasons, acoustic metamaterials are analyzed in this paper.

In the last decade, a new research field has emerged to study Metamaterials [11]. This term refers to materials whose properties are “beyond” those of conventional materials. They are made from assemblies of multiple elements fashioned from composite materials such as metals, foams or plastics. The core concept of metamaterial is to replace the molecules with man-made structures called unit cell. They can be viewed as “artificial atoms”, usually arranged in repeating patterns on a scale much smaller than the relevant wavelength of the phenomena they influence. Several types of metamaterials can be found: electromagnetic metamaterials [12], [13], [14], [15], mechanical metamaterials [16], [17], [18]. Some are artificial three-dimensional structures which, despite being a solid, ideally behave like a fluid. Thus, they have a finite bulk modulus but vanishing shear modulus, ie. they are hard to compress yet easy to deform. And finally, acoustic metamaterials [19], [20], [21], whose effective properties like compressibility or density can be negative. Negative density or compressibility can only be achieved dynamically. For instance, Helmholz resonators driven just above their frequency of resonance lead to negative dynamic compressibility [22]. According to the same principles of wave propagation in periodic structures [23], [24], [25], acoustic metamaterials are tuned to the acoustic wavelength and can be categorized into non-resonant and resonant materials. Resonant metamaterials are generally heterogeneous materials containing a periodic arrangement of elements smaller than the acoustic wavelength: by selectively tuning the material properties of the metamaterial, the elastic or acoustic behavior can be significantly altered from conventional material properties. Resonant metamaterials can be conveniently applied to aircraft interior, airframe noise in naval vessels, and controlling noise in automobiles as the order of magnitude of the wavelength is 1 m and this is much greater than the reasonable thickness of classical damping materials. Work in studying the properties of a heterogeneous material has been carried out at Virginia Tech in the past two decades [26], and has evolved into what is now termed a heterogeneous (HG) metamaterial that will be described better in the following section.

These metamaterials derive their properties not from the properties of the materials they are composed of, but from their newly designed structures with repeating patterns, hence they need to be ‘homogenized’. Indeed, if it is possible to treat them like homogeneous materials with effective properties, their analysis becomes faster and more convenient if the finite element softwares are used.

Finite Element Method (FEM) is well-established and yields accurate results for the structural analysis of any geometrical shape. However, it requires a mesh of all the details of the constituent material. Therefore, when dealing with plates having great numbers of inclusions - such as metamaterials, this method becomes very costly in calculations and time, especially when the macroscopic dimensions of the plate need to be much greater than the characteristic size of the inclusions. Thus, some homogenization methods have been investigated on the last two decades [27], [28]. In particular, Langlet et al. [29] have studied homogenization of passive periodic materials such as a plate periodically perforated across its thickness. In this work, a homogenization method based on the Carrera Unified Formulation (CUF) [30] and Mechanics of Structure Genome (MSG) [31] is investigated. CUF is used to solve the governing equations of MSG for periodically heterogeneous materials. The MSG provides a tool to obtain the complete effective stiffness matrix in a straightforward manner without relying on ad hoc assumptions and minimizing the loss of information between the original heterogeneous cell and the equivalent homogeneous body. This CUF-MSG based homogenization method has been successfully used to find the homogenized mechanical properties of composites [32] and periodic structures [33], in which the unit cell is a cube containing a cylindrical inclusion and the matrix surrounding it.

This research seeks to improve upon the scientific literature by further investigating a heterogeneous material and developing an efficient finite element model to evaluate the acoustic performances of metamaterials at large scale. This concept is unique from previous studies of HG material in which a periodic arrangement of masses within a poro-elastic material is investigated. Furthermore, these numerical finite element models will allow for an advanced understanding of the physics behind the material functionality and they will be used for conducting parametric studies in order to develop more advanced designs and efficient manufacturing of acoustic metamaterials for specific applications.

In particular, this paper presents the results obtained by numerical simulations performed with Actran, an MSC Software based on the finite element method. This is a powerful tool for the acoustic and vibroacoustic analysis of complex structures, accounting for various geometries, load conditions and materials. Moreover, this software allows different types of analyses to be performed, which have been validated through many applications presented in Workshop Series for Actran 17, Acoustics and Vibroacustics Training [34]. A specific model has been created to evaluate the transmission loss properties of the metamaterial. Transmission Loss is one of the key metrics in evaluating acoustic performances of a material and it quantifies the material’s ability to reflect or block sound energy. If transmission loss of a material is high, the sounds emitted on one side of the material tend to stay on this side, and not be heard on the other one, thus the material acts as a barrier for sound. An extensive overview on models for the evaluation of sound transmission loss of panels and comparisons with experimental results is provided in the paper [35] by De Rosa etal.. In this work and other companion articles [36], [37], [38], [39], authors highlight the importance to build good predictive numerical models for virtual simulation of sound transmission loss test in panels with complex geometry or material configurations, such as laminated composites and sandwich panels.

By using Actran model, the effective properties of metamaterial are validated by comparing the transmission loss of the homogenized plate with the results of the heterogeneous one. Then, some studies are performed to investigate the effect of some design parameters on the acoustic performances of HG metamaterial. Finally, the acoustic performances of a composite sandwich panel with metamaterial core will be evaluated with respect to classical sandwich solutions with Nomex core, by keeping the same weight, in order to demonstrate the potentiality of this material as soundproofing insulator for aeronautical applications. Since the characteristic wavelength of noise sources in aeronautics is usually very high, the response of metamaterial is analyzed in low-frequency range (0–500 Hz).

Section snippets

Heterogeneous metamaterial

A heterogeneous (HG) metamaterial is a new class of acoustic metamaterial. It is defined as a composite system consisting of multiple small masses embedded within a passive poro-elastic matrix material. The embedded masses create an array of resonant mass-spring-damper systems within the material that operate at low frequencies where the passive poro-elastic material is no longer effective. By employing the poro-elastic material to provide the stiffness for the embedded masses, the HG

Homogenization of metamaterial properties

The homogenization method here adopted is based on a novel higher-order component-wise beam theory in the framework of the Carrera Unified Formulation (CUF) and yields good results for composites with few calculations [32], [33]. To overcome the limitations of classical models and to deal with complex phenomena, such as torsion, warping, or in-plane deformation, the displacement fields of beam theory are enriched with an arbitrary number of higher-order terms.

The main feature of this method,

Transmission loss

Transmission Loss (TL) is one of the key metrics in evaluating acoustic performances of metamaterials. TL quantifies the amount of energy that is not transmitted through the material and, using HG metamaterial, it can be increased or tuned at specific frequencies while having a mass or volume smaller than conventional acoustic materials. An extensive study of homogenized metamaterial is performed by studying the effects of the volume fraction of the embedded masses on the transmission loss.

In

Parametric study

A numerical parametric study is performed to explore different configurations of a HG metamaterial in terms of volume fraction.

The homogenized plate considered has the same dimensions of those ones in Fig. 9 and different values of volume fractions are considered. Simply supported boundary conditions are here applied to the lateral edges of the plate. For comparison of acoustical performances and to evaluate the effect of inclusions, the Sound Transmission Loss of a full Melamine Foam plate

Sound transmission loss of sandwich plates

A sandwich plate with dimensions 1 × 0.6 × 0.007 m and clamped lateral edges is here considered. The lamination scheme is shown in Fig. 13. The skins are composed by two plies oriented at 0°/90° and the material properties are provided in Table 4.

Two materials are considered for the core: Nomex (see Table 5), that is a typical aeronautical material used for sandwich cores, and metamaterial with a volume fraction of 0.015, that gives an equivalent density equal to the Nomex one ρ=48 kg/m3. The

Conclusions

Sound transmission loss in passive acoustic metamaterials for aeronautical applications has been here studied. The homogenized effective properties of plates made of melamine foam with cylindrical Aluminium inclusions have been evaluated. Results have shown that the homogenization method based on CUF and MSG method permits to efficiently predict the acoustic performances of periodic heterogeneous materials. Then, a parametric study has been performed by varying the volume fraction of inclusions

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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