Mixed third harmonic shear horizontal wave generation: interaction between primary shear horizontal wave and second harmonic Lamb wave

Abstract

The third harmonic shear horizontal (SH) waves in a weakly nonlinear plate provide new possibilities for incipient damage detections. The understanding of their generation mechanism, however, is limited to the intuitive process of cubic self-interaction of the primary SH waves. By considering both the third order and fourth order elastic constants, this paper reports the discovery of a new generation mechanism, referred to as mixed generation, which results from the mutual interaction between the primary SH waves and their induced second harmonic Lamb waves. Compared with linearly cumulative third harmonic SH waves induced by the cubic self-interaction of the primary SH waves, the mixed third harmonic SH wave amplitude also increases with the wave propagating distance but in a wavering manner according to the phase velocity matching condition. Upon establishing a complex-domain superposition method which allows a precise extraction of the third harmonic responses, the significance and the propagating characteristics of the mixed third harmonic SH waves are numerically investigated through finite element simulations. Experiments are then conducted with a dedicated subtraction scheme to highlight the material nonlinearity of interest. A gel test is designed and carried out to identify the two types of third harmonic SH wave components from the measured time-domain signals. Both numerical and experimental results confirm the existence and the significance of the mixed third harmonic SH generation mechanism, which may impact on further applications, especially underwater damage inspections.