Effect of surface/interface stress on nanoscale phononic crystals using complete Gurtin-Murdoch model

Abstract

The gradual miniaturization of acoustic devices requires us to study phononic crystals (PCs) at nanoscale, which should consider the effect of surface/interface stress. The first key point in this study is the complete use of the Gurtin-Murdoch model, and thereby the treatment of the surface displacement gradient term, which was avoided by all previous work on the nanoscale PCs. The second key point is that the dual reciprocity boundary element method is first applied to analyze the band structures of two-dimensional nanoscale PCs. The effect of surface/interface stress on band structures is discussed by investigating four typical nanoscale systems: nanoholes in a soft matrix, nanoholes in a stiff matrix, soft nanoscatterers in a stiff matrix and stiff nanoscatterers in a soft matrix. The numerical results demonstrate that the band structures obtained applying complete Gurtin-Murdoch model ascend comparing with those using simplified model, which enhances theoretical basis for designing nanoscale PCs. Furthermore, the effect of surface displacement gradient term is not obvious for the last three systems, and the displacement gradient term and surface tension should be ignored simultaneously when simplifying calculations. This study can provide good support for the control of hypersound at nanoscale.