  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.
