On the Acoustoelasticity of Backward Lamb Waves in Prestressed Plates

Backward Lamb waves, which exhibit a group velocity that propagates in the opposite direction to their phase velocity, have recently garnered considerable attention for their potential applications in nondestructive testing. Herein we present a theoretical study on backward Lamb waves in the elastic plate subject to prestresses. We demonstrate that the group velocity of the first antisymmetric backward Lamb wave, A3b, decreases with tensile stress, whereas that of the first symmetric backward Lamb wave, S2b, increases. Notably, the sensitivity of A3b to prestress is approximately ten times greater than that of S2b, with a ~5% change in group velocity observed under a uniaxial stress of 100 MPa in steel. This heightened sensitivity facilitates an inverse method for determining prestress levels in elastic plates by examining variations in the A3b group velocity. We also investigate the acoustoelastic properties of zero-group-velocity (ZGV) points, which demarcate the dispersion curves of forward and backward Lamb waves. Our findings indicate that the ratio of resonance frequencies corresponding to A3b and S2b monotonically decreases as uniaxial stress increases, providing an alternative method for prestress assessment. Lastly, we propose an experimental setup for measuring backward Lamb waves and visualize the generation of A3b using dynamic photoelastic techniques. Our research elucidates the acoustoelastic characteristics of backward Lamb waves and highlights their promising utility for stress measurement in elastic plates.