A lumped-mass method is introduced to study the propagation of elastic waves in two-dimensional periodic systems. First, it is used to calculate the band structure of an array of Pb columns in an epoxy background. Second, the method is applied to the same array of Pb columns in a soft rubber background. The results are compared with those calculated with the well-known plane-wave expansion formalism, where the advantages of the lumped-mass method are pointed out and analyzed. These advantages make it possible for easy calculations of band structures of phononic crystals with interfaces of large contrast of elastic constants as well as units of any shapes.

• Received 4 January 2004

DOI:https://doi.org/10.1103/PhysRevB.69.184302