Multiple low-frequency broad band gaps generated by a phononic crystal of periodic circular cavity sandwich plates

We propose a new type of phononic crystal (PnC) composed of a periodic alternation of circular cavity sandwich plates. In the low-frequency regime, the crystal can modulate the propagation of flexural waves. Governing equations are deduced basing on the classical theory of coupled extensional and flexural vibrations of plates. The dispersion relation of the infinite PnC is calculated by combining the transfer matrix method with Bloch theory. The dynamic response of the PnC with finite unit cells is further studied with finite element analysis. An experiment is carried out to demonstrate the performance of the PnC in vibration isolation. Numerical results and experimental results both illustrate that the proposed PnC can generate several wide low-frequency Bragg band gaps providing strong attenuation. The dependence of band gaps upon geometric and material parameters is also analyzed in detail in view of vibration isolation applications.