Metamaterial-based Broadband Elastic Wave Absorber

This article presents modeling and analysis techniques for and reveals the actual working mechanism of longitudinal metamaterial bars as elastic wave absorbers. A metamaterial-based elastic wave absorber can be a uniform isotropic bar with many tiny spring-mass subsystems attached at separated longitudinal locations. In the literature, each cell that consists of a bar segment and an attached spring-mass subsystem is modeled as a discrete system of two degrees of freedom by integration and/or finite difference, and the idealized model becomes a dispersive medium for elastic waves and has a stop band that allows no waves to propagate forward. This work shows that these idealized models can be used only for elastic waves having wavelengths much longer than the unit cell's length. Moreover, it is revealed that a metamaterial-based elastic wave absorber is actually based on the concept of conventional mechanical vibration absorbers, which uses the local resonance of subsystems to generate inertia forces to work against the external load and prevent elastic waves from propagating forward. This concept is extended to design a broadband absorber that works for elastic waves of any wavelengths, including waves having wavelengths shorter than the unit cell's length. Numerical examples validate the design and reveal the cause of stop band. Moreover, the effect of negative effective mass and acoustic and optical modes are explained.