Experimental observation of cumulative second-harmonic generation of Lamb-wave propagation in an elastic plate

The experimental observation of cumulative second-harmonic generation of the primary (fundamental) Lamb-wave propagation is reported in this paper. Using the dispersion relations for Lamb waves and the modal expansion analysis approach for waveguide excitation, a straightforward model has been presented for analysing the physical process of generation of the time-domain pulses of the second harmonics by the fundamental time-domain pulses of the primary Lamb-wave propagation. The physical meaning of the integrated amplitudes, both of the fundamental waves and the second harmonics, is clearly illustrated. Wedge transducers are used to generate and detect the fundamental waves and the second harmonics of the Lamb-wave propagation on the surface of an elastic plate. The clear second-harmonic signals can be observed near the frequency at which Lamb waves have a strong nonlinearity. The amplitudes of the fundamental waves and the second harmonics of the Lamb-wave propagation on the plate surface are measured for different separations between the transmitting and receiving wedge transducers. In the immediate vicinity of a driving frequency at which the fundamental and the double-frequency Lamb waves have the same phase velocities, the quantitative relationships between the second-harmonic amplitudes and propagation distance are analysed. It is observed that the second harmonics of primary Lamb waves grow with propagation distance.