Simulating wave propagation in acoustic metamaterials with isogeometric analysis

Abstract

Finite element analysis (FEA) is commonly used to simulate and design acoustic metamaterials (AMM). Numerical studies employing FEA often rely on Bloch-Floquet analysis of a single unit cell or direct numerical simulations that include many unit cells. Unfortunately, AMM unit cells with fine features necessitate dense computational meshes to resolve the geometry and accurately model wave motion, sometimes prohibiting the use of FEA. Isogeometric Analysis (IGA) is a potential alternative approach to FEA for wave propagation problems. IGA utilizes basis functions that are typically employed in Computer Aided Design (CAD) software, such as B-splines and Non-Uniform Rational B-Splines (NURBS), to represent both the geometry and the wave solution. The direct utilization of the CAD geometry eliminates the need for a separate computational mesh of the geometry and the smoothness of the NURBS basis functions provides increased accuracy per degree of freedom. The latter point is particularly useful for high frequency problems. This talk presents IGA as a means to model AMM behavior and compares results with FEA simulations in terms of total simulation time and accuracy. Finally, we comment on the current limitations of IGA and discuss avenues of future research. [Work supported by the ARL:UT postdoctoral fellowship program.]