Research on flexural wave band gap of a thin circular plate of piezoelectric radial phononic crystals

Piezoelectric thin rings are periodically introduced and placed on a base plate along the radial direction, forming a one-dimensional thin circular plate of piezoelectric radial phononic crystals (CPPRPC). Based on flexural wave equation of thin circular plate and the transfer matrix method, the behavior of flexural waves propagating in CPPRPC is analyzed theoretically and numerically, especially in the band gaps. The transmission curves of CPPRPC and homogeneous-material plate are calculated for comparison. Afterwards finite element simulations are carried out to verify the theoretical results. Furthermore, the effects of the length ratio, thickness ratio, period number and control gain on the flexural wave band gap are discussed in detail. Our results show that there are band gaps of flexural wave in CPPRPC. Structural parameters and outer active control gain have important influences on the band gaps. In particular, low and broad band gaps can be obtained effectively by varying outer active control gain.