Lumped-mass approach for the calculation of band structure of two-dimensional phononic crystals with high contrast of elastic constant

Abstract

With each unit cell replaced by a system of finite freedoms of motion, two_dimensional phononic crystals can be simplified to an infinite discrete periodic system. Therefore, the elastic wave band structures of the two_dimensional phononic crystals can be calculated with a straightforward lumped_mass approach, whose computational cost is much lower than the well_known plane wave expansion(PWE) method. The numerical results of the two methods are in reasonable agreements. As the well_known Gibbs oscillations in the PWE can be eliminated with the lumped_mass method, this new approach is insensitive to the sharp variation of elastic constants on the interfaces inside the phononic crystals. Furthermore, the lumped_mass method can also be used to calculate the band structures of two_dimensional phononic crystals with arbitrary unit shapes easily.