Revealing defect-mode-enabled energy localization mechanisms of a one-dimensional phononic crystal

Abstract

Phononic crystals (PnCs) have received growing attention in recent years, due to their ability to manipulate elastic waves, such as in the case of defect-mode-enabled energy localization. Although previous studies have explored defect modes of PnCs - from phenomenon observations to their potential applications - little effort has been made to date to reveal fundamental mechanisms of defect-mode-enabled energy localization. Thus, this study proposes a lumped-parameter analytical model to reveal the underlying principles of the formation of defect bands of a one-dimensional PnC when a single defect is introduced, or the splitting of defect bands when double defects are introduced. Through the investigation of 1) evanescent wave characteristics in the defect mode shapes, and 2) the asymptotically equivalent behaviors of defect bands and defect-mode shapes with limiting behavior approaches, this study demonstrates a new aspect of why a band gap should be the prerequisite for achieving defect-mode-enabled energy localization. It is confirmed that defect-mode shapes are normal modes, rather than propagating wave modes. The key findings of this study are as follows: 1) the exponentially attenuating characteristics of evanescent waves in a band gap generate a fixed-like boundary condition, which surrounds single or double defects, and 2) mechanical resonance, attributed to the fixed-like boundary condition, leads to the formation and splitting of defect bands.