周期杆中高频纵波的频带分析 Alternative Title Frequency Bands Analysis of the High-frequency Longitudinal Waves in Periodic Rods 潘旭东 Thesis Advisor 郭永强 2015-05-23 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 硕士 Keyword 高频纵波 周期杆 回传射线矩阵法 高阶杆理论 Abstract 周期结构是由平面或空间中的相同基本单元按照平移对称性顺次连接形成的结构。在周期结构中，声子晶体周期性改变结构基本单元的弹性常数，具有优异的动力学特性,为炙手可热的研究课题。当弹性波在声子晶体中传播时，反射波和入射波相互干涉，产生独特的弹性波频带结构，将频率交错的划分为通带和禁带。当弹性波传入声子晶体中时，通带频率范围内的弹性波将毫无损耗地传播，而禁带频率内的弹性波将受到抑制而无法传播。作为一种最简单的声子晶体结构，周期杆结构同样具有声子晶体结构的频带特性。选择周期杆结构为研究对象，避免了复杂的干扰因素，使得关于周期杆频带结构的研究变得方便。目前的研究对杆模型的简化过于粗糙，不能清晰地了解高频纵波在周期杆中的传播；在计算理论上，也缺乏一种能够在高频情况下给出精确计算结果的分析方法。本文将结合回传射线矩阵法以及高阶杆理论，对周期杆中的高频纵波的传播进行分析。本文通过引进高阶杆理论结合回传射线矩阵法，使得高频纵波在周期杆中的传播可以更为精确的被求解出来。还通过比较数值计算得到的结果，得到了几种杆理论弥散曲线的特点，通过比较在不同杆理论下得到的周期多相杆的弥散曲线，得到几种杆理论的适用范围。 Other Abstract Periodic structure is composed of same basic units which are connected in sequence with translational symmetry. The structure has a unique elastic wave band structure property, which can divide frequency range into pass-band and stop-band. When the elastic waves propagate within the pass-band frequency range, elastic waves will be no attenuation, whereas the frequency of the wave within the stop-band will be inhibited and cannot propagate. As the simplest periodic structure, periodic rods also have band characteristic. Using periodic rod structure as the research object avoid the complexity of confounding factors, making research on the band structure of the periodic structure becomes convenient. However, current research on the method of simplified model on the rod is still too rough. Not only hasn’t considered Possion’s effect in high-frequency analysis, but also lack of an exact calculation method which can give precise results at high-frequency condition. In this paper, the method of reverberation-ray matrix (MRRM) combined with modified rod theory is presented for accurately high-frequency analyzing. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/225756 Collection 土木工程与力学学院 Recommended CitationGB/T 7714 潘旭东. 周期杆中高频纵波的频带分析[D]. 兰州. 兰州大学,2015.
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