Mesh sensitivity and experimental verification for randomized arbitrary geometry cavity-based acoustic metamaterials designed with 2D FEM simulations

Acoustic metamaterial development is a rapidly expanding field, which has shown great success in many applied scenarios. The development of acoustic metamaterials is enabled by modelling techniques such as the Finite Elements Method (FEM), which allow for the determination of acoustic parameters of structures with different shapes and sizes. However, complicated geometries within narrow regions of such structures require the consideration of thermoviscous phenomena in modelling, which significantly increases the computational load, at times rendering structural optimization infeasible. This study presents a method for determining acoustic sound absorption parameters of an arbitrary-shape acoustic metamaterial cell in a discretized representation space. The proposed method utilizes a reduction in model dimensionality, using a 2D numerical model to represent a 3D structure, which allows for reduced computational complexity while retaining model accuracy. The method was validated with a simple geometry and compared to methods commonly used in the field including equivalent fluid modelling and the Transfer Matrix Method. The method was validated using impedance tube measurements of generated arbitrary geometry metamaterial cells. A numerical mesh sensitivity study was conducted utilizing 20 generated numerical models. Recommendations regarding the mesh density within a 2D thermoviscous acoustics domain were presented, with acceptable modelling error levels (under 0.5%) achieved by models with strongly reduced mesh density, with a maximum model complexity reduction of 72.4%.