S0302-1-3 Study of cumulative harmonic generation in Lamb waves

Despite its importance in nonlinear ultrasonic measurements, the harmonic generation in Lamb wave propagation is a difficult issue due to the dispersive nature and the multiple mode existence. Based on a systematic analysis of Rayleigh-Lamb frequency equations, the frequencies of Lamb waves which may cause cumulative harmonic generation have been derived in this study. The derived formulas giving angular frequencies, wave numbers, phase velocity and group velocity of the cumulative Lamb modes are given in terms of longitudinal wave velocity, transverse wave velocity, plate thickness and two positive integer numbers. The phase velocity of the fundamental and cumulative harmonic modes is dependent on the ratio of two integer numbers, and there are infinite numbers of such phase velocities at which cumulative harmonic generation is possible. These conclusions can be applied to any elastic material which is isotropic and homogenous.