【作者】 马天雪；

【导师】 汪越胜； 苏晓星；

【作者基本信息】 北京交通大学 ， 固体力学， 2011， 硕士

【摘要】 声子晶体(Phononic Crystal)是一种具有空间周期性结构并呈现弹性波带隙的复合材料。由于其丰富的物理特性,以及在隔音、降噪、减震等领域的应用前景,有关声子晶体的研究目前已成为力学、凝聚态物理、机械工程等众多领域的重要方向之一。本文发展了计算三维声子晶体能带结构的时域有限差分(Finite difference time domain. FDTD)方法,并验证了该方法的精确性与效率。基于所发展的FDTD方法,进行了如下研究：1.通过弹性波波动方程的FDTD差分格式得到了直接影响三维固/固声子晶体带隙的材料参数,包括散射体和基体的横波波速比ct1/ct2、波阻抗比zt1/zt2和泊松比v1、v2。2.研究了材料参数对三维固/固体系带隙的影响,考虑了简立方、体心立方和面心立方三种晶格的体系。结果表明：散射体和基体的波速比和波阻抗比是决定声子晶体带隙的主要材料参数,泊松比相对于这两个参数对带隙的影响较小；带隙仅存在于波阻抗比较大且波速差异相对较小,或波速比较小且波阻抗差异相对较小的两类材料区域内；声子晶体的带隙中心频率随波速比的减小而降低,波速比是调控声子晶体类型(布拉格散射或局域共振)和带隙中心频率的重要材料参数；相对于简立方,体心立方和面心立方晶格的声子晶体更容易产生带隙,且在填充率和材料相同的情况下得到的带隙更宽。3.研究了三维孔隙固体声子晶体的能带特性。由理论分析得到,泊松比是直接决定体系能带结构的材料参数。计算表明,在简立方、体心立方、面心立方三种点阵的体系中,能带结构随泊松比的变化不明显,且不存在完全带隙。更多还原

【Abstract】 Phononic crystals (PNCs) are a kind of composite materials which have periodic structures and exhibit elastic wave band gaps where the propagation of acoustic/elastic waves is fully forbidden. Due to their unique properties and potential applications in sound insulation, noise control, shock attenuation, etc. they have become one of the most important areas in mechanics. condensed matter physics and mechanical engineering, etc. In this thesis, the finite difference time domain (FDTD) method for calculating the band structures of three-dimensional (3D) PNCs is developed, and the accuracy and efficiency of the method are verified. Based on the self-developed FDTD method, we carry out the studies in following aspects:1. The material parameters which determine the band gaps in the 3D solid/solid PNCs are obtained directly from the finite difference form of the elastic wave equations. These material parameters include the transverse wave velocity ratio (ct1/ct2). the acoustic impedance ratio(zt1/zt2) and the Poisson’s ratios v1 and v2.2. The effects of the material parameters on the band gaps in 3D solid/solid PNCs with the simple-cubic (SC). body-centered (BCC) and face-centered (FCC) lattices are studied. The numerical results show that:the transverse wave velocity ratio and the acoustic impedance ratio play more important roles in determining the band gaps than the Poisson’s ratios do:the band gaps appear in the system with large impedance ratio and small mismatch in the wave velocities, or with small wave velocity ratio and small mismatch in the acoustic impedances; the mid-gap frequency decreases as the wave velocity ratio decreases; the wave velocity ratio is the most important parameter which determines the mechanisms (Bragg scattering or local resonance) of the band gaps and the mid-gap frequencies; band gaps are easily opened in the BCC and FCC systems than in the SC system:with the same filling fraction and the material parameters, the band gaps in the BCC-and FCC-latticed systems are generally wider than that corresponding to the SC-latticed system.3. The band structures of the 3D porous PNCs are studied. It is shown that the Poisson’s ratio of the solid host is the unique material parameter which has direct effect on the band structures of a 3D porous PNC. The numerical results show that. in the svstems with the SC, BCC or FCC lattices. the band structure is not sensitive to the Poisson’s ratio. and no full band gap can be generated.更多还原