Torsional wave focusing in cylindrical structures with the conformal gradient-index phononic crystal lens

Abstract

We present torsional wave focusing in cylindrical structures integrated with conformal gradient-index phononic crystal (GRIN-PC) lenses. The mechanical lens modifies the refractive characteristics of propagating waves along the axial direction such that the torsional wave energy focuses at a desired point with an increased amplitude. In this paper, our main goal is to exploit the GRIN-PC concept for amplification of the fundamental torsional wave mode, namely, T(0,1), which is especially favorable in the guided wave ultrasonic testing of pipelines and can extend important structural information over long-range pipelines. To this end, we first study d35 piezoelectric transducer arrays through multiphysics simulations coupling piezoelectric and solid mechanics models and determine the optimal number of transducers to achieve the excitation of torsional plane wave. Two-dimensional Fourier transform as well as the tangential displacement histories around the pipe circumference at various axial positions verify the pure T(0,1) excitation, which is validated with experiments. Next, we design, fabricate, and numerically and experimentally study the conformal GRIN-PC for T(0,1) mode focusing in a range of ultrasonic frequencies, from 30 to 50 kHz. Measurements show that the amplitude of the torsional wave mode is amplified by 39% at the focal point with the presence of the GRIN-PC lens.