Band Gaps in Metamaterial Plates: Asymptotic Homogenization and Bloch-Floquet Approaches

Abstract In this work, we study the transversal vibration of thin periodic elastic plates through asymptotic homogenization. particular, consider soft inclusions and rigid with coatings embedded in a stiff matrix. The method provides general expression for dynamic surface density plate, which compute analytically circular or numerically two-way ribbed plates. Through homogenization, find that band gaps related to in-plane propagating waves occur frequency intervals effective is negative. same result obtained via an analysis Bloch-Floquet problem on unit cell, showing equivalence two approaches. Finally, validate by comparing several examples predicted those from numerical analyses real cell.