Second-Harmonic Generation of a Plane Wave Normally Incident upon a Solid Plate Immersed in Liquid

We theoretically investigate the second-harmonic generation of a plane longitudinal wave normally incident upon a solid plate immersed in liquid. The formulation of the reflected second harmonic is derived within the second-order perturbation. Theoretical analysis and numerical simulation indicate that the reflected second-harmonic amplitude increases sensitively with the increase in the nonlinear acoustic parameter of the plate material at some specific frequencies where the linear reflection coefficient of the normally incident longitudinal wave takes on the minimum value, and that it is independent of the spatial separation between the transmitter/receiver and the solid plate. The results obtained provide a means through which the early state of fatigue-induced damage of the solid plate (characterized by its nonlinear acoustic parameter) can be sensitively assessed by measuring the reflected second harmonic at the specific frequency where the linear reflection coefficient is minimum.