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

Abstract

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.

Enhancing Acoustic Emission Characteristics in Pipe-Like Structures with Gradient-Index Phononic Crystal Lens

“…The stub heights follow a special profile as shown in Figure 2 b, which results in HS distribution of refractive index for the longitudinal L(0,2) mode at a design frequency of 50 kHz [ 33 ]. The design is based on the gradient-index optics theory [ 37 ] where a hyperbolic secant distribution of refractive index within a GRIN lens results in focusing of optical waves at the lens centerline.…”

“…The best HS fit to this distribution has a gradient coefficient of resulting in the first focal point of L(0,1) mode at . The pipe integrated with GRIN lens results in bending of plane wave towards the lens centerline because of the highest refractive index (due to the highest stub height) at that location and it eventually gets focused at the focal point predicted using the GRIN theory as presented in [ 33 ]. The waves bend from the region of lower refractive index (with lower stub heights) towards the region of higher refractive index (with higher stub heights) as per Snell’s law.…”

“… The flow chart of gradient-index (GRIN) phononic crystal lens design for steel pipe where n is the refractive index, is the stub height and is the phase velocity of the propagating elastic wave mode, based on the design methodology in [ 33 ]. …”

“…Since then, researchers has studied planar GRIN lens concept in plate-like structures in both macro [ 27 , 28 , 29 , 30 ] and micro [ 31 , 32 ] scales. More recently, we demonstrated a conformal GRIN lens for pipe-like structures to focus the guided wave energy at sensor locations at the focal points of the lens [ 33 ]. In this paper, we studied the reciprocal behavior of the conformal GRIN lens and leveraged it to convert the AE sources into plane waves for longer transmission of AE signals.…”

Linking Time-Domain Vibration Behaviors to Spatial-Domain Propagating Waves in a Leaf-like Gradient-Index Phononic Crystal Lens

“…Recently, based on destructive interference mechanism, Yan et al designed a phononic crystal with coupled lanes to enhance elastic wave attenuation in the low-frequency regime and the finite element method (FEM) analysis as well as theoretical modeling are presented [9]. Danawe et al designed a conformal gradient-index phononic crystal lens that are integrated within a pipe and applied the amplified guided wave modes to detect the damage of the pipelines, with the validation using the FEM [10]. Zareei et al proposed a continuous profile GRIN lens to focus flexural waves in a thin plate and used the FEM to validate the theoretical design [11].…”