Finite element analysis of the interface/surface effect on the elastic wave band structure of two-dimensional nanosized phononic crystals

In this paper, an interface/surface element is formulated based on the Gurtin-Murdoch interface/surface elasticity theory for accounting the interface/surface effect on the elastic wave propagation in two-dimensional nanosized phononic crystals. The interface/surface element is subsequently incorporated into the finite element procedure for calculating the elastic wave band structure of two-dimensional nanosized phononic crystals with consideration of the interface/surface effect. Elastic wave band structures of two-dimensional phononic crystals comprising a square array of circular or elliptical cylindrical nanoholes embedded in an aluminum matrix are analyzed. Numerical results evidence that the interface/surface effect on the elastic wave band structure can be remarkable when the characteristic size reduces to nanometers.