Metamaterials can be engineered for noise and vibration control through the design of their internal structure. For example, a periodic arrangement of resonant inclusions in a rubber medium applied as a viscoelastic coating on the outer hull of a marine vessel can help improving its stealth. In order to study the properties of a metamaterial, the material parameters of an equivalent homogeneous medium are commonly derived. Retrieval methods are techniques leading to such effective properties using scattering coefficients. In this work, two retrieval methods are applied on a 2D periodic medium with rigid inclusions in an elastic matrix to obtain the effective properties of the constituent unit cell, based on scattering coefficients calculated from numerical simulations (finite element method). Effective wavenumbers and effective impedances are presented along with the displacement fields for the resonance frequencies. Homogenization issues are highlighted, related to the strong hypotheses implied in the different retrieval methods. It is shown that, to predict more accurately the reflection and transmission coefficients for metamaterial samples of given thicknesses, it can be beneficial to combine effective parameters coming from different methods.
