Efficient formulation for band-structure calculations of two-dimensional phononic-crystal plates

Based on Mindlin's plate theory and the plane wave expansion method, a formulation is proposed to study the propagation of Lamb waves in two-dimensional phononic-crystal plates. The method is applied to calculate the frequency band structure of a square array of crystalline gold cylinders in an epoxy matrix with a finite thickness. It is found that complete frequency band gaps for Lamb waves between different pass bands are opened up by tuning thickness of the phononic-crystal plate. The influence of plate thickness on the width of complete frequency band gap is calculated and discussed as well; the existence of frequency stop bands is sensitive to the variation of the thickness of the plate. Finally, we note that the proposed method provides a concise and efficient way in analyzing the frequency band structures of phononic-crystal plates in lower bands.