Quantum analogous spin states to explain topological phase for guided waves in ultrasonic nondestructive evaluation

Spin is a physically observable property that is instrumental for topological behaviors in quantum mechanics. Spin states dictate complex interactions of physical parameters in a topological media during wave propagation. Ultrasonic guided waves are elastic waves that propagate in materials and structures and may also have similar quantum analogous spin states leading to the topological behavior. Traditionally nondestructive evaluation and structural health monitoring use ultrasonic guided waves, but spin states and their topological contributions are not measured or analyzed for damage identification and localization. In this article, the elastic spin state that naturally manifests by the ultrasonic guided waves in an elastic wave guide is explained through quantum analogous derivation. Starting from the fundamentals of Noerther's conservation theorem total angular momentum of guided wave modes is derived. It is shown that even without geometric periodicity guided waves could still have the nonzero spin angular momentum (SAM) density, which may appear from 14 different unique interactions of guided wave potentials. Based on SAM densities spin-orbit interactions in a plate like wave guide is demonstrated where artificially through active actuation, anticlockwise and clockwise spins were created. Further spin states that eventually affect the topological phase is explained through a simulated experiment.