Propagation and Scattering of Coupled Elastic Surface Waves in Curved Structure

这项工作研究了表面波在壳的弯曲弹性表面上的传播，并研究了这些波如何从一个表面耦合到另一个表面。弯曲壳是一种弹性波导，其性质随波长变化缓慢，这些变化是由曲率半径和厚度的变化引起的，而它的两个表面形成弱耦合的表面波波导。在瑞利-兰姆模式下，波场以曲率半径的逆幂渐近展开，每一项随后展开，从而研究了波场的传播。在两个最低瑞利-兰姆模式的传播路径上的振动产生了一个在两个表面之间来回耦合的表面波。当表面波在其中一个表面附近碰到紧凑的不连续面或沿其中一个表面遇到粗糙区域时，表面波所经历的散射也进行了研究。通过对不连续点附近的波场进行局部分析，确定紧凑散射体的反射系数和透射系数，建立了紧凑散射体的模型。通过计算表面波的衰减来模拟粗糙度。这项工作的结果将与爱荷华州立大学无损评估中心的现有数据进行比较。高速旋转的涡轮叶片和用于输送石油或天然气的管道都是常见的弯曲结构，超声波检查的损伤如疲劳开裂或腐蚀。涡轮叶片的疲劳裂纹通常发生在其根部，这个位置并不总是肉眼可见的。管道的腐蚀可以从其内部表面开始，除非关闭一段管道，否则无法检测到腐蚀。这项工作研究了如何使用表面波来检测这些弯曲的弹性壳结构，表面波首先在外表面传播，然后在内表面传播，最终返回到外表面，在那里它们被拾取。这些波探测到内部表面的损伤，并将信息传递到外部。超声波检查还必须对损伤的严重程度作出估计。通过模拟小表面裂纹的散射或由腐蚀引起的衰减，这项工作可以解释表面波从一个表面到另一个表面所携带的信息，从而对损伤进行定量估计。

DMS-9500723 Harris This work investigates the propagation of surface waves over the curved elastic surfaces of a shell and studies how these waves couple from one surface to another. The curved shell is an elastic waveguide whose properties change slowly with wavelength, these changes being caused by the varying radii of curvature and thickness, while its two surfaces form weakly coupled surface-wave waveguides. The propagation is studied by asymptotically expanding the wavefields in inverse powers of the radii of curvature with each term subsequently expanded in the Rayleigh-Lamb modes. The beating over the propagation path of the two lowest Rayleigh-Lamb modes gives rise to a surface wave that couples back and forth between the two surfaces. The scattering that a surface wave experiences when it strikes a compact discontinuity near one of the surfaces or encounters a region of roughness along one of them is also studied. The compact scatterer is modeled by assigning it reflection and transmission coefficients determined from a local analysis of the wavefields near the discontinuity. The roughness is modeled by working out the attenuation to the surface wave. The results of this work will be compared to existing data at the Center for Nondestructive Evaluation at Iowa State University. Turbine blades rotated at high speeds and pipelines used to carry oil or natural gas are among the common curved structures ultrasonically inspected for damage such as fatigue cracking or corrosion. Fatigue cracks in a turbine blade often occur at its root, a location not always visually accessible. Corrosion to a pipeline can begin at its interior supface where it cannot be detected unless a section of the line is shut down. This work investigates how these curved, elastic shell structures can be inspected using surface waves that propagate first over the exterior surface, then over the interior surface, ultimately returning to the exterior surface where they are picked up. Th ese waves detect damage to an interior surface and carry that information to the exterior. Ultrasonic inspections must also give an estimate of the seriousness of the damage. By modeling scattering from a small surface crack or attenuation caused by a patch of corrosion, this work enables the information carried by a surface wave from one surface to another to be interpreted to give quantitative estimates of the damage.