Transferable Analytical Model of Phononic Bandgap in Cross-Hole Phononic Crystals

We numerically and theoretically investigate Phononic Crystals (PnC) with cross holes in a plate material. We show that phononic bandgap can be tuned precisely by changing structural parameters in the PnC, and the vibrational modes at lower and upper edges of the bandgap frequency can be well reproduced by three types of analytical model; an effective spring-mass model, flexural wave mode of thin plate, and the Bernoulli-Euler theory for vibrating beam. The width and position of the designed bandgap are confirmed by an experimental measurement of transmission spectra for a thin plate with the PnC structure.