The Band Structure In 2D Resonant Phononic Crystal

In recent years, there has been an increasing interest in the studies of acoustic or elastic waves propagating in the periodic elastic artificial composite materials which is called phononic crystal (PC). Due to the existence of the frequency band gaps, acoustic or elastic waves in the phononic crystal show some special properties, implying a great potential application. In the present thesis, we have studied the behavior of the finite two-dimensional resonant phononic crystal.(1). We briefly introduce the principle of Bragg scattering in phononic crystals,and indicate the characteristics in Bragg scattering-phononic crystals. We also give some method of calculated the band structure of two-dimensional phononic crystals,we compare the advantage and disadvantage of these methods.(2). We briefly introduce the principle of local resonance in phononic crystal, and indicate the characteristics in local resonance -phononic crystals.(3). We study the wave propagation of a 2D local resonant sonic crystal consisting of polymethyl methacrylate cylinders in air background. Band structures are calculated by using the finite element method with a periodic boundary condition. Band structures of the sonic crystal with a Helmholtz resonant (HR) defect are discussed and compared. The frequenciesof the defect band depend strongly on the geometric size of the defect.(4). The finite element method are used in the condition of two-dimensional Al-resonant cavity phononic crystal in air. The results showed that: the band structure of Al-resonant cavity phononic crystal are very different from the normal phononic crystals,the band structure of Al-resonant cavity phononic crystal have an additional resonance gap. The aperture size of the cavity, the inner diameter size, and structure of the constant changes will affect the location and width of the band gaps.