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.