Quantitative Study on Energy Distribution and Mode Conversion of Ultrasonic Guided Waves Interacting with Stepped and Tapered Transition Regions

Abstract

Ultrasonic guided waves (UGWs) are extensively used in structural health monitoring and nondestructive testing, particularly for complex structures such as lap joints, icing plates, and composite interfaces. This study comprehensively investigates the mode conversion, reflection, and transmission of UGWs both at the stepped and tapered transition region, where geometric discontinuity causes energy redistribution among various modes of reflected and transmitted UGWs. The Frequency Domain Finite Element method is employed to quantitatively analyse the mode energy distribution across a frequency range of 0~3 MHz, with Mode S0 as the incident UGW. The results demonstrate that the energy distribution of transmitted UGW modes follows the phase velocity matching principle, whereas the reflected UGW energy exhibits no discernible pattern. Both the linearly and curvedly tapered transition regions improve the energy transmission efficiency by mitigating mode mismatches. Furthermore, increasing the length-to-thickness ratio of linearly tapered transition enhances the energy transmission, reaching over 99% at all frequencies when the ratio exceeds 5. The validation is conducted with the Time Domain Finite Element method and experiment. These findings provide valuable insights for optimizing the selection of UGWs, improving the accuracy and effectiveness of monitoring at stepped and tapered structures.

Keywords: Ultrasonic guided wave, stepped transition, mode conversion, tapered transition