Second-order harmonic generation of Lamb wave in prestressed plates

Abstract

This paper investigates the second-order harmonics generation associated with propagation of Lamb wave in pre-stressed plates. The second-order harmonic phenomena appear in a weakly non-linear medium due to material and geometry nonlinearities. This study proposes finite element (FE) models to incorporate stress constitutive equations formulated by Murgnahan's strain energy function. The model is used to take into account the stress effect on second-order harmonic generation of Lamb wave propagation in weakly nonlinear media. The developed FE model is first validated against two-dimensional (2D) analytical solutions. A three-dimensional (3D) FE model is then developed and utilised to study more realistic problems, such as the rate of accumulation of the non-linear parameter β' at different wave propagation angles when the plate is subjected to a bi-axial stress and the effect of the applied stresses on second-order harmonic generation in a plate with a fatigue crack. The results demonstrate that the applied stresses can notably change the value of β' in different directions. The finding of this study can gain physical insight into the physical phenomenon of stress effect on second-order harmonic generation of Lamb wave. Thus, the current study opens an opportunity for the development of a new non-destructive stress evaluation technique for plate- and shell-like structural components. Moreover, the new technique can be easily incorporated with existing guided wave based-SHM systems and provide information regarding the change of the stress conditions. Such additional information can significantly improve the structural life prognosis and reduce risk of failures.