Non-destructive evaluation of prestress in plates by nonlinear guided waves

This paper investigates the diagnostic potential of guided Rayleigh-Lamb waves in a homogeneous, elastic, isotropic prestressed plate in the light of the finite strain theory. This theory accounts for the fact that strains are not infinitesimal and involves the use of the Green Lagrange strain tensor. Since the strains are not infinitesimal, an appropriate expression of the strain energy must be adopted. Three different states of prestress are considered: uniaxial stress in the direction of the wave propagation, uniaxial stress orthogonal to the direction of wave propagation, and quasi-isotropic stress state. Two different approximations of the model are considered, that is first and second-order. The first-order approximation provides linearized equations of motion enabling to investigate the variation of group velocity as a function of the initial state of prestress. The second-order approximation is used to develop an analysis of the secondary wave field based on the perturbation approach and accounting for synchronicity requirements. This enables to define quantitative relations between the amplitude of the nonlinearity-driven second-harmonic plate wave and the state of prestress. These relations can be used to evaluate, nondestructively, the level of prestress in plate-like structures.