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基于光子晶体相似的二维声子晶体特性研究

Characteristics of Two-Dimensional Phononic Crystals Based on the Similarly of Photonic Crystals

【作者】 赵芳

【导师】 苑立波;

【作者基本信息】 哈尔滨工程大学 , 光学工程, 2005, 硕士

【摘要】 近年来,对声波在周期性弹性复合介质中传播的研究越来越受到人们的关注,尤其是对声子禁带(或称声波带隙)特性,即处于声波带隙频率范围内的振动或声波被禁止在声子晶体中传播的研究更为活跃。这种具有弹性波带隙的周期性复合材料称为声子晶体。通过对声子晶体的研究不仅可以使我们发掘其潜在的广泛应用,例如声学滤波器、高精度的无振动环境以及新型声波换能器和声导纳等,而且还可以使我们更深入的理解物理学中声子的安德森局域化问题。 本文,我们利用平面波展开法构建了二维声子晶体的理论计算模型,详细地研究了平面波展开法的理论和算法,并采用Matlab高级编程语言对其进行了独特、有效的执行。利用平面波法我们探究了二维声子晶体能带结构特性,并分析了各种材料和结构参数对带隙的影响。 利用平面波展开法结合超原胞法详细地研究了声子晶体的缺陷态特性。研究结果表明:点缺陷可以把声波俘获在缺陷处,使其无法向外传播,相当于微腔;而线缺陷可以使处于禁带频率范围内的声波沿通道进行传播,形成所谓的声波导。在对两种基本缺陷研究的基础上,我们进一步构造了同质位错结,并分别研究了横向位错结和纵向位错结两种情况下的局域模。我们发现,横向位错效应与线缺陷相似,它可以使处于禁带频率范围内的声波沿位错通道进行传播,形成声波导;纵向位错效应则类似于点缺陷,位错线两边三个最接近的“原子”形成腔,从而能够产生局域模。 最后,我们研究了二维声子晶体异质结的界面态。我们构造了三种不同类型的异质结:SCSC异质结、SCSS异质结和RRTC异质结。结果表明:前两种异质结中不存在界面态,必须将两个子晶格沿着界面横向拉开或者侧向滑移才能在带隙中产生传导模。另外,横向或侧向相对位移的大小将影响带隙的宽度和传导模的位置,因此,我们可以通过调节相对横向或侧向位移来人为的控制异质结中的传导模。但是,RRTC异质结能够在不做任何晶格移动的情况下就产生界面传导模,这个结果有别于其它声子晶体异质结的性质。产生界面传导模的原因可以归结为RRTC异质结的结构特点,它在界面两边的子晶体具有不同类型的布拉菲格子,加大了界面处的畸变程度。

【Abstract】 In recent years there has been growing interest in the propagation of acoustic (AC) or elastic (EL) waves in periodic elastic composite materials known as phononic crystals, which have phononic band gaps. Of particular interest is the existence of band gaps in which sound and vibration are all forbidden. The motivation for these studies is to better understand the Anderson localization of sound and vibrations in composite media, as well as their numerous engineering applications such as elastic/acoustic filters, vibrationless environments for high-precision mechanical systems or the design of new transducers and sonar.In this dissertation, the plane-wave expansion method (PWM) is developed for the 2D phononic crystals’ modeling and simulation. The theory and algorithm of PWM are studied in detail and implemented by Matlab in a unique and efficient approach. PWM is used to obtain the gap information of 2D phononic crystals. Several material and structural parameters are shown to affect the band gap.Effects of defects in phononic crystals are studied in detail by using the plane-wave method combined with the supercell technique. Results show that point defects can pin the sound waves to the defect, then sound can not escape, and form resonator, whereas line defects can mold the flow of sound, which lie in the bandgap, along the channel and form the so called waveguides. Based on the studies on the two basic defects, we ulteriorly construct the homogeneity dislocation structures, and investigated transverse dislocation structures and longitudinal dislocation structures respectively. We found that transverse dislocation structures, acted as the line defect, can form waveguides too; while, longitudinal dislocation structures can form a cavitylike void surrounded by the three nearest cylinders around the interface, which acted just as the point defect.Finally, we studied the guide modes formed in two-dimensional phononic crystal heterostructures. We construct three different types of heterostructures: SCSC heterostructure, SCRC heterostructure and RRTC heterostructure. Results show that localized interface states are absent in the former two heterostructures, they can be created either by lateral lattice slipping or by increasing the interface separation; the absolute gap width and the position of guide modes strongly depend on the relatively transverse and longitudinal gliding displacement, so we can artificially control the guide modes by adjusting the relatively transverseand longitudinal gliding displacement of lattices in a heterostructure. But the RRTC heterostructure can produce guide modes in bandgap without any relative gliding or transverse displacement. This feature is quite different from other phononic crystal heterostructures. The reason can be ascribed to the prototype phononic crystals have different lattices, which augments the aberrance at the interface.

  • 【分类号】O735
  • 【被引频次】3
  • 【下载频次】487
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