Theoretical analysis and experimental observation of frequency mixing response of ultrasonic Lamb waves

In this work, we analyze theoretically and observe experimentally the frequency mixing response induced by the collinear interaction of two primary Lamb waves with different frequencies in an isotropic and homogenous plate. The internal resonance conditions for generating the combined harmonics are analyzed by using a perturbation approach and a normal-mode-expansion technique for waveguide excitation. The second- and third-order combined harmonics generated by the collinear wave mixing of two primary Lamb waves propagating in a specimen are analyzed, and the existence of the combined harmonics at specific frequencies is predicted. An experimental procedure is proposed to measure the combined harmonics induced by the collinear cross-interaction of the two specific primary Lamb waves at given frequencies. The theoretical prediction of the appearance of the combined harmonics at the specific mixing frequencies is consistent with experiment. The theoretical analysis and experimental observation provide a clear physical insight into the frequency-mixing response induced by the collinear cross-interaction of two primary ultrasonic Lamb waves.