Bandgap properties in locally resonant phononic crystal double panel structures with periodically attached pillars

The locally resonant (LR) phononic crystal double panel structure made of a two-dimensional
periodic array of a two-component cylindrical LR pillar connected between the upper and
lower plates is proposed, and the bandgap properties of the structure are investigated theore-
tically in this paper. The band structures, displacement fields of eigenmodes and transmis-
sion power spectrums of the corresponding 8×8 finite structure are calculated by the finite
element method. Numerical results and further analysis demonstrate that a band gap with a
low starting frequency and a wide band width is opened by the coupling between dominant
vibrations of the pillars and plate modes of the upper and lower plates when the vibration
source and the receiver are considered on different sides of the structure. By comparing the
band structures and displacement fields of the double panel and those of the single plate
with the same parameters, many common characteristics are displayed. Then, the influence
of geometrical parameters on the band gap are studied and understood with the help of a
simple ‘spring-mass’ model.