Beam-steering ultrasonic guided waves in a bone-mimicking plate by time-delaying the excitation of the elements in a multi-element array: a numerical study

Abstract

We present a numerical simulation of the beam-steering of ultrasonic guided waves in an isotropic and viscoelastic solid plate, which mimics bovine cortex. The excitation was modeled by a group of five finite-size emitters, each exercised a normal force to the bone plate. Beam steering was achieved by delaying the emitters’ firing. The simulation technique was implemented by a semi-analytical finite element scheme to compute the wave fields. At small steering angles, the simulated time-offset signals show mainly two groups of arrivals. The first group is the fast-traveling and high-frequency bulk waves and the second one is slow-traveling and low-frequency guided waves. The fast-traveling waves gradually diminish with increasing steering angles, in agreement with the excitation function of the source influence theory. The frequency-phase velocity dispersion maps also illustrate the phenomenon. The study has demonstrated that the lowest order Lamb asymmetrical mode, A 0, which is useful for bone characterization, can best be excited when the cortical bone thickness is thin, the beam angle is large, and the excited frequency is low.