A Simple Method for the Design of 1-D MEMS Flexural Phononic Crystals

We present a simple and computationally inexpensive method to design 1-D MEMS flexural phononic crystals (PnCs) with assigned width and central frequency of the acoustic bandgap based on the analysis of the characteristic polynomial of the acoustic transmission matrix of the crystal elementary cell. Our analysis shows that a high acoustic contrast does not necessarily lead to wide bandgaps, unless the modulation of the mechanical properties is properly chosen. We also demonstrate that the acoustic attenuation inside the bandgap, which is an important design target, is essentially predetermined once that the bandgap width and center have been chosen. The method can be valuable for fast design of PnC devices with applications spanning from sensors to filters and resonators.