Modeling and Analysis of Ellipticity Dispersion Characteristics of Lamb Waves in Pre-stressed Plates

In this research, based on the weak nonlinear elasticity theory and finite deformation theory, a dynamic equation of guided waves in pre-stressed plates is established. Legendre orthogonal polynomials expansion method is employed to analytically solve wave equations. The dispersion curves and particle trajectory are obtained without root-finding algorithm. The solution is validated by comparing with the superposition of partial bulk wave method, and its convergence properties are analyzed. The effects of the pre-stress states on particle trajectory and ellipticity dispersion curves are investigated. Results confirm that the behavior of particle trajectory and ellipticity dispersion depends not only on the pre-stress states but also on frequency and mode. Next, ellipticity dispersion curve of fundamental Lamb modes with various stress state and propagation directions are calculated. Finally, the sensitivity of ellipticity as an indicator of stress is also analyzed. These results provide useful reference for the development of innovative nondestructive testing method for pre-stress states based on Lamb waves.