Second order ultrasonic guided wave mutual interactions in plate: Arbitrary angles, internal resonance, and finite interaction region

Abstract

The sensitivity of ultrasonic wave interactions to material and geometric nonlinearities makes them very useful for nondestructive characterization. The ability of guided waves to interrogate inaccessible material domains, be emitted and received from a single surface, and penetrate long distances provides capabilities that bulk waves do not. Furthermore, mutual interactions between waves propagating in collinear or non-collinear directions provide excellent flexibility as to which types of waves are used, as well as their frequencies and interaction angles. While the interaction of bulk waves is well established, the mutual interaction of guided waves traveling in arbitrary directions in a plate is not and requires a general vector-based formulation. Herein, by vector-based calculations, the internal resonance criteria are formulated and evaluated for waves propagating in arbitrary directions in a plate. From the analysis, it is found that non-collinear guided wave interactions transfer power to secondary guided wave modes that is impossible for collinear interactions, which is completely analogous to bulk waves. For the case of tone burst-pulsed wave packets at nonzero interaction angles, the wave interaction zone has a finite size, and its size is dictated by many factors, including, for example, the group velocities of the waves, interaction angle, pulse duration, and dispersion. An analytical model is introduced for finite-sized interaction zones and used to demonstrate the effect of group velocity mismatch on the generation of secondary waves. In addition, finite element simulations are compared to the analytical model and provide additional insight into secondary wave generation and propagation.