声表面波在周期栅阵中传播特性的变分原理研究
文献类型：学位论文
| 作者 | 徐方迁 |
| 学位类别 | 博士 |
| 答辩日期 | 2004 |
| 授予单位 | 中国科学院声学研究所 |
| 授予地点 | 中国科学院声学研究所 |
| 关键词 | 声表面波 变分原理 色散关系 禁带 有限元 |
| 其他题名 | A Study Based upon Variational Principle of the Properties of Surface Acoustic Waves Propagating under Periodic Metal Grating |
| 中文摘要 | 本文从波动方程和边界条件出发，根据陈东培和H.A.Haus理论、采用变分原理分析了声表面波在压电晶体表面短路金属栅中的传播特性。在分析力学负载对反射栅的反射系数贡献时，我们发现不同材料栅条其晶体对称性是不一样的，反射系数的理论计算公式也随之改变。我们详细推导了不同晶体对称性栅条反射系数的理论计算公式，首次给出四方4／姗，六角6／mInm金属栅条和三角3m沟槽等反射·系数计算公式。论文将陈东培和H.A.Haus理论从一般的Rayleigh波推广到sH型表面波，并根据Abbott's COM方程及Plessky’s COM方程分析了sH型表面波在栅阵中的色散特性。给出了SH型表面波在栅阵中色散关系的具体求解方法。为SH型表面波器件的理论分析和设计开辟了一个新的途径。根据COM理论，解释了由陈东培和H.A.Haus理论得到的色散关系表达式物理意义，即该表达式表示的是色散曲线禁带上边缘和禁带下边缘频率与Bragg中心频率之差。通过Poynting定理将陈东培和H．A．Haus理论公式中的二维积分转为平面有限元问题，从而在陈东培和H.A.Haus理论中成功地使用有限元方法分析厚电极栅阵的反射特性。为了将陈东培和H.A.Haus理论用于二指栅阵中声表面波传播特性的分析，我们对这种栅阵的静电场问题作了理论研究。给出了关于二指栅阵Floquet散射分量的具体理论计算公式，也就是将Datt。等人关于单指栅阵静电场理论推广到二指栅阵。根据上面的理论研究结果，本文编制了相应的数值计算程序，提取了有关特征参数。本文的理论研究工作丰富和发展了陈东培和H.A.Haus理论，使压电晶体中关于声表面波的变分方法不再局限于一般的Rayleigh波，而能用于SH型表面波，能够分析厚电极栅条和二指栅阵。作者希望前人以及本文的工作使压电晶体中的变分方法引起人们广泛关注，并在未来的声表面波理论研究中发挥更大的作用。 |
| 英文摘要 | Originated from the equation of fluctuation and the boundary conditions and based on D.P,Chen and Haus theory, a variational principle was used to investigate surface acoustic waves passing through piezoelectric crystal with short-circuited gratings. Analyzing strip reflection coefficient produced by mechanic loading, we discovered Closed-form expressions of it for different crystal symmetry class are not uniform. With detailed deduction of closed-form expressions of the different crystal symmetry classes, we put forward, for the first time, the closed-form expressions of strip reflection coefficients of tetragonal 4/mmm, hexagonal 6/mmm and trigonal 3m crystal etc. We extended D.P,Chen and Haus theory for general Rayleigh-type SAWs to SH-type SAWs and hence discussed the dispersion characteristics of SH-type SAWs propagating on periodic metallic grating structures by means of Abbott's COM equation and Plessky's COM equation. Solution to dispersion relation of SH-type SAWs is obtained and a new approach for the theoretical analysis and design of SH-type SAWs devices has been developed. Using COM theory, the physical meaning of the dispersion relation derived from D.P,Chen and Haus theory was explained, i.e. this relation stands for the upper edge or the lower edge of the stopband, The problem of a double integral in D.P,Chen and Haus theory is transformed into that of two-dimensional finite element by virtue of Poynting theorem. Consequently, finite element method is successfully applied to analysis on reflection characteristics of metallic gratings with finite thickness in D.P,Chen and Haus theory. To apply D.P,Chen and Haus theory to the discussion of SAW propagation in periodic metallic grating structures with two fingers per period, we have studied the electrostatic problem of this gratings. Closed-form expressions for the scattered Floquet components perturbed by double-electrode gratings are given. Namely, Datta's theory for the electrostatic field of single-electrode gratings is extended to that of double-electrode gratings. Effectiveness of the above theoretical analysis is demonstrated with results of the numerical analysis for the Rayleigh SAW modes and SH-type SAW modes. This paper extends and develops D.P,Chen and Haus theory. The variational method for SAW propagation in piezoelectric crystal now can be applied to not only Rayleigh SAW modes but also SH-type SAW modes. In addition, it can be used to analyze the effects of grating with finite electrode thickness and the properties of double-electrode gratings. The authors hope that this variational method will arouse peoples's attentions because of previous study and our works and play more important role in the SAW research in future. |
| 语种 | 中文 |
| 公开日期 | 2011-05-07 |
| 页码 | 113 |
| 源URL | [http://159.226.59.140/handle/311008/836]  |
| 专题 | 声学研究所_声学所博硕士学位论文_1981-2009博硕士学位论文 |
| 推荐引用方式 GB/T 7714 | 徐方迁. 声表面波在周期栅阵中传播特性的变分原理研究[D]. 中国科学院声学研究所. 中国科学院声学研究所. 2004. |
入库方式： OAI收割
来源：声学研究所
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