Bound Modes in the Continuum in Architected Beams

This work demonstrates the existence of a novel class of localized elastic modes, namely bound modes in the continuum (BICs), in architected elastic beams. Current designs to achieve localized modes in periodic structures require bandgaps and suffer from energy leakage into the surrounding. BICs have the unique property that their mode amplitude goes to zero outside a compact region and they thus have zero leakage. In addition, their frequencies lie in pass bands and the designs thus do not require any bandgaps. Such mode shapes arise due to specific stringent conditions on the geometry of the structure. This work considers beams with an array of periodic masses. By adding carefully engineered defects, we derive a systematic procedure to achieve BICs in our considered structures in the context of Euler-Bernoulli beam theory. This procedure yields a family of BICs by varying the location and geometry of the defects. Our predictions are complemented with numerical simulation and experimental measurements that demonstrate the existence of BICs. Such wave confinement has potential application as filters in sensors and in elastic wave signal processing.