柱状固体分层介质中的声导波
文献类型：学位论文
| 作者 | 崔寒茵 |
| 学位类别 | 博士 |
| 答辩日期 | 2009-05-31 |
| 授予单位 | 中国科学院声学研究所 |
| 授予地点 | 声学研究所 |
| 关键词 | 导波 频散曲线 激发强度 柱状固体分层介质 Stoneley波 |
| 其他题名 | Guided waves in a cylindrical multi-layered solid medium |
| 学位专业 | 声学 |
| 中文摘要 | 研究柱状固体分层介质中导波的传播特性具有重要意义，如重大工程中为防止山体滑坡和岩石基础破碎而大量使用的锚杆，如何采用声学方法对锚杆的锚固质量进行无损检测就是一个柱状固体分层模型中的声传播问题。这方面的研究工作并不多见，而且大都集中在对导波频散特性的分析上，忽视了研究导波激发强度的重要性。事实上并不是所有的导波模式都可以被激发出来，哪些模式可以被激发出来并接收到？哪些模型的激发强度比较大？这些问题是从导波频率曲线图中得不到的。只有结合频散特性和激发强度特性，才能更全面地了解和掌握各种导波模式在不同频段内的传播规律，才能有效识别和区分接收信号中的多种导波模式。 本文研究了柱状固体分层介质中导波的传播特性，不仅分析了频散特性，而且重点研究了激发强度特性。一般来说，导波在柱状固体分层介质中的频散方程是复数的超越方程，只能用数值方法求解。我们构造了两个新函数（贝塞耳函数的线性组合），使导波的频散函数总为实函数，从而可以方便的使用二分法，快速准确地求出某频率范围内的所有导波模式。 首先分别研究了导波在两层、三层、四层和五层柱状固体分层介质中，轴对称传播的纵波模式、非轴对称传播的弯曲波和高阶弯曲波模式的频散特性。所有导波模式都是高度频散的，在截止频率处的相速度值等于其最外层介质的横波速度值；根据各模式频散曲线的高频趋向性可分为两类：简正模式（Normal Mode）和Stoneley模式。简正模式的相速度和群速度频散曲线在高频时都趋近于各层介质中最小的横波速度值（Vsmin）；而Stoneley模式的高频速度极限值小于Vsmin。 在频散特性的研究基础上，进一步分析了在三种模拟声源：对称点源、轴向力源和径向力源的作用下，激励出的导波模式的激发强度特性，分别探讨了各模式的激发强度随频率和径向半径的变化关系。从导波位移分量幅度谱可知：不同的激发频率范围内，激励出的主导模式不同；一般来说前几阶模式的幅度较大，为模型中的主导模式；每一个模式达到幅度最大值的频率都在该模式群速度最小值对应的频率附近，这一特性有利于判断出导波的有效激发频率范围。另外，从导波在径向横截面上的幅度分布图可知：简正模式表现出能陷特征，它们的位移分量幅度峰值大多集中具有最小横波速度值的介质层中；而Stoneley模式的径向和轴向位移分量幅度都随远离界面的距离增大而逐渐减小，在无限远处衰减到零，是柱面交界面上的界面波。在分析并比较了各种导波模式的传播特性后，我们发现：径向力源激励出的最低阶弯曲波模式是适合检测的模式，它的截止频率最低，且在低频时的激发强度比其它模式大很多，因此可以在低频处被激发出来，而且信号较强容易被区分和识别。 本文另一个主要创新点是对两柱状固体介质交界面上Stoneley模式的传播特性研究。目前对简正模式的研究相对较多。简正模式只能存在于硬地层模型（即最外层介质的横波速度大于Vsmin的模型）中，然而大部分锚杆锚固体系中最外层介质的横波速度较小，例如煤矿中的锚杆，应该用软地层模型来模拟。软地层模型中没有任何简正模式，但可能存在Stoneley模式，因此对柱面上的Stoneley模式进行研究非常必要，然而此方面研究较为少见。我们首先研究了各介质参数对导波模式的影响，得到了柱状固体分层介质中Stoneley模式的存在条件：在两层柱状固体介质中，当其材料参数组合与存在Stoneley波的两半无限大平面介质的材料参数组合相同时，存在柱面上的Stoneley模式；在三层柱状固体介质中，仅当最内层和中间层介质的材料参数组合与存在Stoneley模式的两半无限大平面介质的材料参数组合相同，并且最外层横波速度值大于Stoneley波速时，才存在柱面上的Stoneley模式。其次探讨了在两层柱状固体介质中，具有反常频散曲线Stoneley模式的存在条件，并比较了具有正常/反常频散曲线的导波模式传播特性的不同。另外结合Stoneley模式的频散和激发强度特性可知，三层柱状固体介质中仅存在沿第一界面（即最内层和中间层介质的交界面）传播的Stoneley界面波。通过分析Stoneley模式和简正模式的激发强度特征可知，当柱状固体分层介质的材料参数组合满足Stoneley波的存在条件时，Stoneley模式的激发强度总是远远大于简正模式的，简正模式的波形会被Stoneley模式的完全覆盖掉，也就是说，仅有Stoneley模式可以被激发出来。 |
| 英文摘要 | Propagation of guided waves in cylindrical multi-layered elastic solid medium is an interesting research topic. One important application is ultrasonic non-destructive evaluation (NDE) for inspection of the rockbolts which are installed to reinforce ground in mining and civil engineering structures. Although some studies have been reported on this topic, most of them focus on the dispersion characteristics without considering the excitation mechanisms. If one guided mode with good dispersion characteristics has less excitation intensity than other modes, it will be difficult to receive. Therefore, the excitation intensity is an important physical quantity for guided waves, yet little attention has been paid on it. In this paper, guided waves propagated in a cylindrical multi-layered elastic solid medium are studied. Not only are the dispersion characteristics analyzed further, but also the excitation mechanisms of all guided modes are investigated as keystone. The dispersion equation of the guided waves is generally a plural function for a real axial propagation velocity. We transform it into a real dispersion function, and employ the bisection technique to find all the real roots, in order to give all the dispersion curves of the guided waves robustly. All the guided modes propagated in double-, three-, four-, and five-layered models are studied. Each one of the guided wave dispersion curves begins at its cutoff frequency where phase velocity is equal to the shear velocity of the outside layer. And it finally meets its high-frequency phase velocity asymptote which is either equal to the smallest shear velocity (named as Vsmin) among all the layers for the normal waves, or less than Vsmin for the Stoneley waves. The excitation intensities of the guided waves excited by the symmetric point source, axial and radial force sources are investigated. They are highly relied on excitation frequency and radial position. Thus dominant modes are different with different excitation frequencies. Moreover, intensity of each mode reaches its maximum around the frequency where the group velocity reaches its minimum and finally tends to zero at high frequency. The displacement distributions of the normal waves along the radial direction are complicated. However, intensities of the Stoneley waves, which are interfacial waves propagated in cylindrical interfaces, decay with radial distance far from the interface into the outside layer, and finally approach zero at infinity. Moreover, the lowest branch of flexural guided waves excited by radial force source holds the promise for NDE of rock bolts. It can be excited out with the largest intensity in the lower frequency range. Furthermore, the excitation and propagation characteristics of the Stoneley waves in cylindrical multi-layered solid medium are investigated. As former studies are focused on using the normal guided waves propagated in the hard cladding model whose shear velocity of the cladding is larger than that of the rockbolt. However, most rockbolts are inserted in the soft claddings. In this case, there is no normal guided wave existed, yet may have the Stoneley waves under certain conditions. Therefore, the investigation of the Stoneley waves’ behavior is significant but seldom reported. First, the existence conditions for the Stoneley wave in cylindrical interface are received by discussing the effects of both the material combination and shear velocity of the cladding on the existence of Stoneley wave in double- and three-layered cladding models. In the double-layered models, the Stoneley modes in cylindrical interface are highly dispersive and merely exist in the model whose acoustical parameters satisfied the existence condition of the Stoneley waves. And the normal modes merely exist in the “hard cladding” model in which the cladding’s shear velocity is larger than the rod’s. While in the three-layered models, the Stoneley mode in cylindrical interface merely exist in the model whose acoustical parameters of the inner and the middle layers satisfied the existence condition of the Stoneley waves in a planar interface, and the shear velocity of the outside layer is larger than the Stoneley velocity, here is the phase velocity of the Stoneley wave in the planar interface. And the normal modes merely exist in the model whose shear velocity of the outside layer is larger than the smallest shear velocity (Vsmin). Then, the dispersion curves of the longitudinal and flexural Stoneley waves in the soft and hard cladding models are numerical predicted by using the bisection technique. Moreover, the excitation characteristics, ignored in previous references, of the Stoneley waves are analyzed and compared with those of the normal waves. It is predicted that the guided waves received in actual measurement should be the Stoneley waves, while the normal waves are seriously covered by the Stoneley waves and impossible to be seen in full-waveforms, when the Stoneley wave existence condition is satisfied. |
| 语种 | 中文 |
| 公开日期 | 2011-05-07 |
| 页码 | 172 |
| 源URL | [http://159.226.59.140/handle/311008/460]  |
| 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 | 崔寒茵. 柱状固体分层介质中的声导波[D]. 声学研究所. 中国科学院声学研究所. 2009. |
入库方式： OAI收割
来源：声学研究所
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