Prediction of transmission, reflection and absorption coefficients of periodic structures using a hybrid Wave Based - Finite Element unit cell method

This paper presents a hybrid Wave Based Method - Finite Element unit cell method to predict the absorption, reflection and transmission properties of arbitrary, two-dimensional periodic structures. The planar periodic structure, represented by its unit cell combined with Bloch-Floquet periodicity boundary conditions, is modelled within the Finite Element Method, allowing to represent complex geometries and to include any type of physics. The planar periodic structure is coupled to semi-infinite acoustic domains above and/or below, in which the dynamic pressure field is modelled with the Wave Based Method, applying a wave function set that fulfills the Helmholtz equation and satisfies the Sommerfeld radiation condition and the Bloch-Floquet periodicity conditions inherently. The dynamic fields described within both frameworks are coupled using a direct coupling strategy, accounting for the mutual dynamic interactions via a weighted residual formulation. The method explicitly accounts for the interaction between the unit cell and the surrounding acoustic domain, also accounting for higher order periodic waves. The convergence of the method is analysed and its applicability is shown for a variety of problems, proving it to be a useful tool combining the strengths of two methods.