Multistable metamaterial on elastic foundation enables tunable morphology for elastic wave control

Abstract

We present a strategy for continuously and reversibly tuning the propagation of elastic waves in one-dimensional systems without need for persistent external stimulation. The general approach places a bistable metamaterial on an elastic substrate which is subsequently deformed via prescribed boundary displacements. The internal substrate deformation, which is shaped by a prescribed spatial variation in elasticity, is reflected in the overlaying metamaterial and facilitates the reconfiguration of bistable elements over isolated regions. As each configuration is associated with a unique stiffness, these regions represent an adjustable, meso-scale morphology amenable to tuning elastic waves. The essential bistability is characterized by an asymmetric, double-welled equipotential energy function and is developed by mechanical rather than phenomenological means. The asymmetry provides for the unique, configuration-specific (stable) equilibrium stiffnesses; the equipotential promotes reversibility (i.e., no one configuration is energetically preferred). From a uniform metamaterial-substrate system, we demonstrate the utility of our strategy by producing a waveguide with shifting passband and a metamaterial with variable unit cell morphology.