Novel computational tools and optimisation strategies offer an unprecedented framework to explore large design spaces within a short time frame. In the scope of material design, these new possibilities have completely revolutionized the research horizon, leading amongst other things to controlled anisotropy media with a finer granularity than ever seen before. However, a question arises regarding the manufacturability of such media which most of the time relies on 3D printing and the agreement between modelled and printed geometry. In the recent years, the authors published several articles on the properties of Kelvin Cell packings and the possibility to control their anisotropy. In the last few months, an effort towards printing the designed media has been made in search for experimental validation of the numerical results. This contribution describes the printing process for kelvin cell packing samples with controlled anisotropy and analyses their agreement with the model both from a geometric and from a physical response standpoint. Depending on the advances of current research, information on the dynamic behaviour of such systems will be discussed.

The dynamic behaviour of a novel anisotropic cellular micro-structural geometry derived from the basic symmetric Kelvin cell is discussed for varying relative density. The cells are arranged in a cubic array and the dynamic response is studied in a classical seismic mass setup using beam elements to represent the ligaments of the cell. The eigenfrequencies and the eigenmodes of the cellular array are computed together with forced response simulations where a proportional damping model of the Young's modulus for the cell ligaments is assumed. The frequency dependence of the damping is based on a fractional derivative representation. Using a recently developed inversion method, equivalent, homogenised solid material models of the cellular array are discussed with the associated equivalent elastic properties given in terms of the 21 elastic constants of the Hooke's tensor. For the equivalent solid material models, the eigenfrequencies and eigenmodes are computed, and forced response simulations are performed assuming the same type of proportionality in the damping as the cellular array, for the same seismic mass setup. The correlation, between the eigenfrequencies and the eigenmodes, shows an overall interesting agreement between the cellular and the equivalent solid model for the quite complex deformation shapes observed. The forced response results indicate that the equivalent solid modelling accurately represents the global dynamics of the anisotropic cellular array, but needs to be further refined when local shearing deformation within the individual cells starts to be dominating.

Numerical methods are central to modern engineering and the Finite Element Method (FEM) specifically is used in a variety of domains and for countless applications. One of the main challenges of using FEM lies in the choice of parameters to generate the mesh. This is particularly the case in acoustics. Indeed, for the phenomena to be correctly modelled, the mesh parameters must be chosen in concordance with the frequency range of interest. So far, the choices regarding the mesh are mostly guided by past experience or widely accepted guidelines (for instance 7-10 points per wavelength when using quadratic elements). In this contribution, we explore the use of reinforcement learning to construct and refine a FEM mesh. This technique implies that the machine is learning how to complete a given task based solely on the so-called state of the environment (including a measure of the error on the result). The key aspect of this research is to challenge the traditional guidelines used for acoustic problems by letting a machine explore and converge without human intervention. The overall strategy will be introduced and demonstrated on simple problems, the results compared with pre-existing recommendations and the challenges ahead will be briefly presented.

Multilayer panels consisting of a load carrying structure, a porous material for thermal and acoustic insulation and an interior trim panel is a very common type of design for vehicles. Weight as well as total build height are usually limiting constraints on the design. The idea of using an anisotropic porous material instead of an isotropic one to improve the sound transmission loss without adding a lot of weight or thickness is explored in the paper. By using a state space formulation of the transfer matrix method transmission loss it is possible to include anisotropic material properties in the calculation. The anisotropic material is modelled by a combination of a simplified analytical model for the acoustic losses and inverse estimation of the 21 independent elastic constants of the Hooke's tensor. The porous material, which has typical dimensions possible to 3D print, is based on a Kelvin cell micro model that has a controlled degree of anisotropy.

Multilayer panels consisting of a load carrying structure, a porous material for thermal and acoustic insulation and an interior trim panel is a very common type of design for vehicles. Weight as well as total build height are usually limiting constraints on the design. The idea of using an anisotropic porous material instead of an isotropic one to improve the sound transmission loss without adding a lot of weight or thickness is explored in the paper. By using a state space formulation of the transfer matrix method transmission loss it is possible to include anisotropic material properties in the calculation. The anisotropic material is modelled by a combination of a simplified analytical model for the acoustic losses and inverse estimation of the 21 independent elastic constants of the Hooke’s tensor. The porous material, which has typical dimensions possible to 3D print, is based on a Kelvin cell micro model that has a controlled degree of anisotropy. 

In the recent years, our team has been working to identify key aspects of anisotropy in porous media. More than just characterising their anisotropic properties, we're interested in generating cellular media with completely designed anisotropic properties. The results of these studies have partly been published and more are to come. In this presentation, we'll present an overview of this work and how it ultimately ties to acoustics. We will introduce the key findings,discussed specific results that can be achieved and provide context and details related to the strategy developed to address the tasks.

The properties of the materials used for building sound proofing systems are known to exhibit large variations. These may lead to significant differences in the acoustic responses within a given material batch, particularly when resistive screens are used as a surface component for a multi-layered absorbing panel. In such thin films, it is mostly the thickness and the flow resistivity, but in some cases also the porosity, that are difficult to control in the production process. All these potential variations influence the acoustic response of the complete panel. In the present contribution, a method to isolate and evaluate the effect of uncertainties in a film is proposed. Using a transmission line approach, it is shown to be possible to predict the modification of the response induced by the uncertainties. The proposed technique is then adapted to determine uncertainty envelopes of the absorption coefficient, for experimentally acquired responses, that are closer to measured envelopes as compared to those generated using Monte Carlo simulations or simplified approaches. The method is tested both on numerical and experimental cases and shows, in both cases, a very good agreement with the reference solutions. Unlike Monte Carlo approaches, the proposed method does not require a massive computational effort which makes it suitable for real life applications.

The purpose of this work is to check if additive manufacturing technologies are suitable for reproducing porous samples designed for sound absorption. The work is an inter-laboratory test, in which the production of samples and their acoustic measurements are carried out independently by different laboratories, sharing only the same geometry codes describing agreed periodic cellular designs. Different additive manufacturing technologies and equipment are used to make samples. Although most of the results obtained from measurements performed on samples with the same cellular design are very close, it is shown that some discrepancies are due to shape and surface imperfections, or microporosity, induced by the manufacturing process. The proposed periodic cellular designs can be easily reproduced and are suitable for further benchmarking of additive manufacturing techniques for rapid prototyping of acoustic materials and metamaterials.

Simple geometric distortions applied to the isometric Kelvin cell structures, (the tetrakaidecahedron), are shown to result in equivalent materials with anisotropic Hooke's tensors. The equivalent material models are estimated using a recently published inversion method where the 21 independent elastic constants of the Hooke's tensor are identified. In these cell geometries, some of the faces of the Kelvin cell have been twisted and/or tilted. Numerical experiments suggest that the equivalent material models of the distorted cells exhibit variations in compression, shearing, shear-compression and shear-shear coupling moduli, which are shown to be continuous functions of the degree of twist and tilt applied. When twist and tilt are combined, it is demonstrated that full anisotropy in the elastic properties may be generated. A rotational symmetry without symmetry planes, but having either a tetragonal or a monoclinic elastic symmetry is discussed. Four cell geometries, one isometric and three distorted, were manufactured using masked stereolithography 3D printing technology and measured in a laboratory compression set-up. Results from numerical simulations are compared to the experimental in terms of the compressive modulus.

The paper discusses the vibro-acoustic behaviour of a recently proposed novel anisotropic cellular foam geometry derived from the basic symmetric Kelvin cell geometry. The associated equivalent elastic material properties are estimated based on a recently developed inversion method, in terms of the 21 elastic constants of the Hooke's tensor. The dynamic behaviour of the cellular material configuration and its homogeneous model by applying the equivalent material properties are studied under arbitrary excitation. The correlation between the vibro-acoustic behaviour, foam density, and material anisotropy is studied based on finite element simulations. High correlations of eigenfrequency and eigenmode shapes between the target cellular foam model and the equivalent solid model are found. A set of empirical relations are proposed, linking the micro-structure in low to high relative density for the anisotropic cellular geometries investigated. Potential applications in vibro-acoustic of the proposed anisotropic foam are discussed