The Generation Mechanism Of The Nonlinear Lamb Wave And The Evaluation Index For Early-stage Damage In Materials

In this dissertation,the generation mechanism and conditions of the accumulative second harmonic and the zero-frequency were studied and the evaluation index of material early stage damage was proposed.First,the propagation of finite-amplitude waves in an isotropic,homogenous,stress-free elastic plate is investigated theoretically.Weak material and geometric non-linearities are considered,and perturbation method is employed to obtain solutions of the non-linear equations of motion for harmonic generation in the guide-wave.Solutions for zero-frequency,sum-frequency,difference-frequency,and the second-harmonic components are obtained by means of modal decomposition method.Two conditions for internal resonance are identitfied: power or energy transfer from the primary wave mode to the second harmonic mode,and phase velocity matching.The second harmonic and zero-frequency only can be symmetric and can be excited by both a symmetric and an antisymmetric primary mode.Second,based on identical particle and virtual particle hypothesis,the control condition of two-dimensional velocity is derived,and the propagation of linear waves is described at the atomic scale using interatomic potential functions.Furthermore,the generation mechanisms of zero-frequency,sum-frequency,difference-frequency,and the second-harmonic components are studied by considering the effects of lattice anharmonicity and dislocation.The study shows that the lattice distortion caused by lattice anharmonicity and dislocation induces the nonlinear virtual particles,which are the key factor in generating zero-frequency,sum-frequency,difference-frequency,and the second-harmonic waves,and then early-stage nonlinearities or micro-damages,e.g.,dislocation,lead to the increase of the nonlinear virtual particles inducing the obvious zero-frequency,sum-frequency,difference-frequency,and the second-harmonic waves.Third,Meshless Local Petrov-Galerkin-Eshelby Method simulations were able to clarify the theoretical results.Finally,the zero-frequency,the second-harmonic and the energy attenuation of primary wave can be used as the evaluation index of early-stage nonlinearities or micro-damages in structures and materials.This research is valuable which will be useful in the field of structural health monitoring and non-destructive evaluation when using nonlinear Lamb waves.