Optimization of acoustic porous material absorbers modeled as rigid multiple microducts networks: Metamaterial design using additive manufacturing

Abstract

This research presents a strategy to enhancing sound absorption in porous acoustic metamaterials through the optimization of micro-duct networks. The study employs a combination of analytical and numerical methods, systematically adjusting micro-duct diameters within a 2D grid to optimize absorption coefficients at specific frequency bands. The Finite Element Transfer Method (FETM) is utilized for modeling, supported by a multi-objective function influenced by the surface impedance of the network. This approach ensures practical applicability and manufacturability of the designed metamaterial. A significant aspect of the study is the development of an analytical mobility matrix for each microduct, integrated through the Transfer Matrix Method using the visco-thermal dissipation theory. This integration results in a physically coherent model, for which a semi-analytical sensitivity analysis related to the microduct diameters can be directly performed. The optimization employs the Method of Moving Asymptotes (MMA), effectively managing the complexity associated with a large number of design variables. Subsequently, the optimized structure is adapted into a 3D grid, facilitating prototype creation using Additive Manufacturing Technology (AMT) with a specific polymer material. The research methodology is validated through four distinct test cases, each demonstrating the efficacy and adaptability of the optimization tools and techniques. Experimental validation, conducted using an impedance tube, indicates a significant shift in the first absorption maximum from 2500 Hz to 1000 Hz, achieved without altering the material thickness. Additional validation through 3D Finite Element Method (FEM) modeling, which includes visco-thermal effects, further confirms the acoustic efficiency of the final designs. While the potential for achieving lower sub-wavelength conditions is recognized, the study opts for simpler structures, considering the current limitations of 3D printing technology. This study contributes to both theoretical understanding and practical application in acoustic material design, emphasizing the potential for customizing materials to specific frequency ranges. The integration of FETM modeling with MMA provides a systematic and effective approach for optimizing acoustic materials, particularly in enhancing absorption at lower frequencies.