Frequency Mixing Response of Ultrasonic Guided Waves in Plate

Abstract

It has been shown that the use of frequency mixing response has some unique advantages over the nonlinear ultrasonic technique based on the higher harmonic generation, such as frequency selectivity, which can intentionally avoid receiving unexpected harmonic components induced by the instrumental systems. In addition, the feature of spatial selectivity of scanning wave mixing technique can readily be used to locate the region of damage. In this paper, frequency mixing response induced by the collinear interaction of two primary Lamb wave modes with different frequencies in an isotropic and homogenous plate is theoretically analyzed and experimentally observed. The second- and third-order combined harmonics generated by the collinear wave mixing of two primary Lamb waves propagating in a given specimen are analyzed, and meanwhile the existences of the combined harmonics at some specific frequencies are predicted. An experimental procedure is proposed to measure the combined harmonics that are induced by the collinear cross-interaction of the two specific primary Lamb wave modes at some given frequencies. 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 wave modes. Considering the difficulty for experimental verification for theoretical predictions in a systematic manner, characteristics of nonlinear frequency response for Lamb waves mixing are also examined numerically in this paper. Results indicate that the synchronism and symmetric property of selection of primary Lamb wave mode pair significantly affect the generation of combined harmonic waves at mixing frequencies. These numerical investigations clearly illustrate the physical process and nonlinear feature of Lamb waves mixing. It is shown that the controllable potential of mode pair selection for Lamb waves mixing, which is of practical significance for nonlinear acoustic scanning in large specimen.