Conformal gradient-index phononic crystal lens for ultrasonic wave focusing in pipe-like structures

We explore a conformal gradient-index phononic crystal lens integrated within a pipe to amplify guided wave modes toward improved ultrasonic inspection of pipelines. The proposed conformal lens is composed of an array of cylindrical steel stubs attached to the outer surface of a steel pipe, which are tailored according to the hyperbolic secant profile of refractive index in the circumferential direction of the pipe. Hence, the ultrasonic guided wave energy is focused in the axial direction of the pipe and amplified at the focal point of the lens. Refractive indices are calculated using dispersion curves obtained from the finite element simulations of the stubbed unit cells, and the curved lens is designed for the second longitudinal wave mode of the pipe, which is commonly used in guided wave testing. The proposed lens design is implemented on a steel pipe, which is typically used in the distribution networks utilized in cities, and simultaneous focusing of longitudinal wave modes in a broad frequency range is verified through both numerical models and experimental measurements.

我们探索了一种集成在管道内的共形梯度折射率声子晶体透镜，以放大导波模式，从而改进对管道的超声检测。所提出的共形透镜由附着在钢管外表面的一系列圆柱形钢短柱组成，这些短柱是根据管道圆周方向上的折射率双曲正割分布定制的。因此，超声导波能量在管道轴向聚焦，并在透镜焦点处放大。折射率是利用从带短柱的单胞有限元模拟中获得的频散曲线计算得出的，并且这种曲面透镜是为管道的第二种纵波模式设计的，该模式在导波检测中常用。所提出的透镜设计在钢管上实现，这种钢管通常用于城市的配水网络中，并且通过数值模型和实验测量验证了在较宽频率范围内纵波模式的同时聚焦。