A blueprint for truncation resonance placement in elastic diatomic lattices with unit cell asymmetry

Abstract

Elastic periodic lattices act as mechanical filters of incident vibrations. By and large, they forbid wave propagation within bandgaps and resonate outside them. However, they often encounter “truncation resonances” (TRs) inside bandgaps when certain conditions are met. In this study, we show that the extent of unit cell asymmetry, its mass and stiffness contrasts, and the boundary conditions all play a role in the TR location and wave profile. The work is experimentally supported via two examples that validate the methodology, and a set of design charts is provided as a blueprint for selective TR placement in diatomic lattices.