Study On The Bandgaps Of Two-dimensional Quasi Periodic Phononic Crystals

Phononic crystal (PNC) is a new kind of acoustic functional material which exhibits elastic wave band gaps. The essential property of the PNC is its band gaps which have numerous potential engineering applications such as acoustic filters, control of vibration isolation, noise suppression and design of new transducers. Therefore, it caused widespread concern of the domestic and foreign scholars in recent years.The quasi-periodic phononic crystal (QPNC) with short-range disorder and long-range order property is a state between ordered and completely disordered systems. The loss of the translational invariance means that the Bloch theory is no longer applicable. So the unit cell can’t be used to study the band structures of the QPNCs. The high symmetry degree of the QPNCs makes the disorder degree stronger, and the wave localization phenomena will occur when the elastic wave propagating in the system. In this thesis, the following problems for elastic waves propagating in two-dimensional (2D) QPNCs are studied:1. Combined with the supercell method, the finite element software COMSOL Multiphysics is used to calculate the band structures of the2D8-fold solid/solid QPNC. Both the anti-plane and in-plane modes are considered. Different supercells with different number of the scatterers are chose to calculate the dispersion curves of the QPNC and the results are compared with those of its periodic average structure (PAS). The influences of the supercell on the band structures and the wave localization phenomenon are discussed combined with the modal distributions. The influences of the filling fraction on the band structures are discussed. The results show that the band structures of the2D8-fold solid/solid QPNC can be well calculated by the supercell containing its center pattern; several flat bands appear nearby the upper and lower boundaries of the band gaps which mean elastic wave localization phenomenon occurs under the frequencies of these flat bands. But the bands appear in the band gaps are false bands.2. Combined with the supercell method, the finite element software COMSOL Multiphysics is used to calculate the band structures of the2D12-fold solid/solid QPNC. Both the anti-plane and in-plane modes are considered. The supercell containing its center pattern is chose to calculate the dispersion curves of the QPNC and the results are compared with those of its periodic average structure (PAS). The wave localization phenomena is discussed combined with the modal distributions. The influences of the filling fraction on the band structures are discussed. The results show that the band structures of the2D12-fold solid/solid QPNC can be well calculated by the supercell containing its center pattern; several flat bands appear nearby the upper and lower boundaries of the band gaps which mean elastic wave localization phenomenon occurs under the frequencies of these flat bands. But the false bands similar to pass bands appear in the band gaps.3. The wave propagation of the2D8-fold solid/fluid QPNC are studied by experiment. The transmission spectrum of different samples are obtained. And the band structures of the QPNC are calculated by the finite element method. The experimental results are consistent with those of FEM means that it’s valid to use this experimental system to study the elastic wave propagation in the QPNC, and the band gaps of the2D solid/fluid8-fold QPNC can be well calculated by the supercell containing its center pattern. The band structures obtained by FEM show that there is no obvious flat bands in the band gaps of the2D solid/fluid QPNC.