Abstract
Plate wave propagation in two-dimensional locally resonant sonic materials (LRSMs) is theoretically analyzed. The well-known plane wave expansion method for a periodic elastic structure recast based on the Mindlin plate theory and a finite element (FE) method are employed to calculate the frequency band structures of plate waves. The results of the two methods are compared. The FE method is further used to analyze the resonant eigenmodes and attenuation spectrum of the plate waves propagating through a finite LRSM. Numerical results show that complete band gaps of plate waves exist in the frequency range of two orders of magnitude smaller than those in typical sonic crystals where complete band gaps are produced by Bragg scattering. The attenuation spectrum of plate waves in a finite-size LRSM containing eight rows of locally resonant unit structures is in good agreement with the band gaps predicted using the frequency band structure.