Controlling the thickness dependence of torsional wave mode in pipe-like structures with the gradient-index phononic crystal lens

The fundamental torsional wave mode, T(0,1), is typically preferred in monitoring defects in long-range pipe-like structures due to non-dispersive and low attenuation characteristics such that the wave packet is not distorted with distance. However, the sensitivity of T(0,1) wave mode depends on the defect type and orientation. While it is highly sensitive to cracks along the axis of pipes, the sensitivity to detect thickness change is low as T(0,1) wave mode generates tangential displacement motion around the pipe circumference. In this study, a gradient index phononic crystal (GRIN-PC) lens is integrated into a steel pipe to manipulate its dispersion characteristics such that the phase velocity of T(0,1) wave mode is affected by the overall change in pipe thickness. The modified behavior of T(0,1) wave mode within the GRIN-PC lens region increases the damage detection capability of T(0,1) wave mode. Numerical models involving a parametric unit cell study indicate that the phase velocity of T(0,1) wave mode decreases as the thickness of the pipe with the GRIN-PC lens decreases, in contrast with the conventional pipe. The signal difference coefficient (SDC) is applied to the acquired signal from the focal point of GRIN-PC lens to quantify the uniform thickness change. Full-scale wave propagation simulations involving solid mechanics coupled with the piezoelectric actuation demonstrate that the SDC increases as the thickness decreases. The numerical results are validated with experiments using three steel pipes with different wall thicknesses.