Inverse band gap design of elastic metamaterials for P and SV wave control

Abstract

We describe a systematic approach for engineering the dispersive properties of elastic metamaterials in order to band-gap, at user-defined frequency ranges, the propagation of elastic waves, accounting simultaneously for both P and SV waves. To this end, we focus on the inverse design of a metamaterial’s unit cell, and cast the design problem as an optimization problem, driven by the desired band gap, and constrained only by the cell’s dispersive characteristics; the latter are expressed in terms of the Floquet–Bloch eigenvalue problem. Numerical results in the time-domain, using metamaterial assemblies with only narrow periodicity, demonstrate that the engineered metamaterial attains the desired behavior. Extensions to wave steering, shielding, and other wave-control applications, follow naturally.