Two- and Three-Dimensional Holey Phononic Crystals with Unit Cells of Resonators

Y.F. Wang[1][2], Y.S. Wang[1], L. Wang[2]
[1]Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing, China
[2]Department of Mechanical Engineering, Østfold University College, Halden, Norway

We show in this paper that by careful design of the geometry of the resonators, complete bandgap with relatively low center frequency can be obtained for 2D and 3D Phononic Crystals with resonators. The generation of the bandgap is due to the local resonance of the unit cell. Spring-mass and spring-pendulum models are developed to predict the boundaries of the complete bandgap. The predicted results are in general agreement with the numerical results. The geometry of the resonator has significant influences on the bandgaps. This study is relevant to the optimal design of the bandgaps in light porous materials. More detailed structures of the resonant unit cell can be designed by following the same idea of the present paper