Investigation into the Acoustic Properties of Polylactic Acid Sound-Absorbing Panels Manufactured by 3D Printing Technology: The Influence of Nozzle Diameters and Internal Configurations

Sound-absorbing panels are widely used in the acoustic design of aircraft parts, buildings and vehicles as well as in sound insulation and absorption in areas with heavy traffic. This paper studied the acoustic properties of sound-absorbing panels manufactured with three nozzle diameters (0.4 mm, 0.6 mm and 0.8 mm) by 3D printing from three types of polylactic acid filaments (Grey Tough PLA; Black PLA Pro; Natural PLA) and with six internal configurations with labyrinthine zigzag channels (Z1 and Z2). The absorption coefficient of the sample with the Z2 pattern, a 5.33 mm height, a 0.6 mm nozzle diameter and with Black PLA Pro showed the maximum value (α = 0.93) for the nozzle diameter of 0.6 mm. Next in position were the three samples with the Z1 pattern (4 mm height) made from all three materials used and printed with a nozzle diameter of 0.4 mm with a sound absorption coefficient value (α = 0.91) at 500 Hz. The highest value of the sound transmission loss (56 dB) was found for the sample printed with a nozzle size of 0.8 mm with the Z2 pattern (8 mm height) and with Black PLA Pro. The extruded material, the nozzle diameter and the internal configuration had a significant impact on the acoustic performance of the 3D-printed samples.

Design and Additive Manufacturing of Porous Sound Absorbers-A Machine-Learning Approach

Additive manufacturing (AM), widely known as 3D-printing, builds parts by adding material in a layer-by-layer process. This tool-less procedure enables the manufacturing of porous sound absorbers with defined geometric features, however, the connection of the acoustic behavior and the material's micro-scale structure is only known for special cases. To bridge this gap, the work presented here employs machine-learning techniques that compute acoustic material parameters (Biot parameters) from the material's micro-scale geometry. For this purpose, a set of test specimens is used that have been developed in earlier studies. The test specimens resemble generic absorbers by a regular lattice structure based on a bar design and allow a variety of parameter variations, such as bar width, or bar height. A set of 50 test specimens is manufactured by material extrusion (MEX) with a nozzle diameter of 0.2 mm and a targeted under extrusion to represent finer structures. For the training of the machine learning models, the Biot parameters are inversely identified from the manufactured specimen. Therefore, laboratory measurements of the flow resistivity and absorption coefficient are used. The resulting data is used for training two different machine learning models, an artificial neural network and a k-nearest neighbor approach. It can be shown that both models are able to predict the Biot parameters from the specimen's micro-scale with reasonable accuracy. Moreover, the detour via the Biot parameters allows the application of the process for application cases that lie beyond the scope of the initial database, for example, the material behavior for other sound fields or frequency ranges can be predicted. This makes the process particularly useful for material design and takes a step forward in the direction of tailoring materials specific to their application.

Design, Experimental and Numerical Characterization of 3D-Printed Porous Absorbers

The application of porous materials is a common measure for noise mitigation and in room acoustics. The prediction of the acoustic behavior applies material models, among which most are based on the Biot-parameters. Thereby, it is expected that, if more Biot-parameters are used, a better prediction can be obtained. Nevertheless, an estimation of the Biot-parameters from the geometric design of the material is possible for simple structures only. For common porous materials, the microstructure is typically unknown and characterized by homogenized quantities. This contribution introduces a methodology that enables the design and optimization of porous materials based on the Biot-parameters and connects these to microscopic geometric quantities. Therefore, artificial porous materials were manufactured using 3D-printing technology with a prescribed geometric design and the influence of different design variables was investigated. The Biot-parameters were identified with an inverse procedure and it can be shown that different Biot-parameters can be influenced by adjusting the geometric design variables. Based on these findings, a one-parameter optimization procedure of the material is set up to maximize the absorption characteristics in the frequency range of interest.

A parametric model order reduction technique for poroelastic finite element models

This research presents a parametric model order reduction approach for vibro-acoustic problems in the frequency domain of systems containing poroelastic materials (PEM). The method is applied to the Finite Element (FE) discretization of the weak u-p integral formulation based on the Biot-Allard theory and makes use of reduced basis (RB) methods typically employed for parametric problems. The parametric reduction is obtained rewriting the Biot-Allard FE equations for poroelastic materials using an affine representation of the frequency (therefore allowing for RB methods) and projecting the frequency-dependent PEM system on a global reduced order basis generated with the proper orthogonal decomposition instead of standard modal approaches. This has proven to be better suited to describe the nonlinear frequency dependence and the strong coupling introduced by damping. The methodology presented is tested on two three-dimensional systems: in the first experiment, the surface impedance of a PEM layer sample is calculated and compared with results of the literature; in the second, the reduced order model of a multilayer system coupled to an air cavity is assessed and the results are compared to those of the reference FE model.

The Partition of Unity Finite Element Method for the simulation of waves in air and poroelastic media

Recently Chazot et al. [J. Sound Vib. 332, 1918-1929 (2013)] applied the Partition of Unity Finite Element Method for the analysis of interior sound fields with absorbing materials. The method was shown to allow a substantial reduction of the number of degrees of freedom compared to the standard Finite Element Method. The work is however restricted to a certain class of absorbing materials that react like an equivalent fluid. This paper presents an extension of the method to the numerical simulation of Biot's waves in poroelastic materials. The technique relies mainly on expanding the elastic displacement as well as the fluid phase pressure using sets of plane waves which are solutions to the governing partial differential equations. To show the interest of the method for tackling problems of practical interests, poroelastic-acoustic coupling conditions as well as fixed or sliding edge conditions are presented and numerically tested. It is shown that the technique is a good candidate for solving noise control problems at medium and high frequency.

A residue-based mode selection and sorting procedure for efficient poroelastic modeling in acoustic finite element applications

Analysis of three-dimensional sound propagation in porous elastic media with the Finite Element (FE) method is, in general, computationally costly. Although it is the most commonly used predictive tool in complex noise control applications, efficient FE solution strategies for large-size industrial problems are still lacking. In this work, an original procedure is proposed for the sorting and selection of the modes in the solution for the sound field in homogeneous porous domains. This procedure, validated on several 2D and 3D problems, enables to reduce the modal basis in the porous medium to its most physically significant components. It is shown that the size of the numerical problem can be reduced, together with matrix sparsity improvements, which lead to the reduction in computational time and enhancements in the efficacy of the acoustic response computation. The potential of this method for other industrial-based noise control problems is also discussed.

A modal-based reduction method for sound absorbing porous materials in poro-acoustic finite element models

Structural-acoustic finite element models including three-dimensional (3D) modeling of porous media are generally computationally costly. While being the most commonly used predictive tool in the context of noise reduction applications, efficient solution strategies are required. In this work, an original modal reduction technique, involving real-valued modes computed from a classical eigenvalue solver is proposed to reduce the size of the problem associated with the porous media. In the form presented in this contribution, the method is suited for homogeneous porous layers. It is validated on a 1D poro-acoustic academic problem and tested for its performance on a 3D application, using a subdomain decomposition strategy. The performance of the proposed method is estimated in terms of degrees of freedom downsizing, computational time enhancement, as well as matrix sparsity of the reduced system.