Time-domain analysis and experimental examination of cumulative second-harmonic generation by primary Lamb wave propagation

Abstract

Within the second-order perturbation approximation, the physical process of cumulative second-harmonic generation by the primary Lamb wave propagation has been investigated in the time domain. Based on the preconditions that the transfer of energy from the primary Lamb wave to the double frequency Lamb wave is not zero and that the phase velocity matching condition is satisfied, we focus on analyzing the influence of mismatching of the group velocities on the generation of the second harmonic by propagation of a primary Lamb wave tone burst with a finite duration. Our analysis indicates that the time-domain envelope of the second harmonic generated is dependent on the propagation distance when both the duration of the primary Lamb wave tone burst and the group velocity mismatch are given. Furthermore, it can be concluded that the integrated amplitude of the time-domain second harmonic, which quantifies the efficiency of the second-harmonic generation, grows with the propagation distance even when the group velocity matching condition is not satisfied. The experimental examination has been performed, and it verifies our theoretical analysis.

Effect of precipitate-dislocation interactions on generation of nonlinear Lamb waves in creep-damaged metallic alloys

“…[14][15][16][17][18][19][20][21][22][23][24][25][26] In the past years, some theoretical and experimental studies of nonlinear Lamb waves have been reported. [14][15][16][17][18][19][20][21][22][23][24][25][26] It is found that the generation of cumulative higher harmonics in Lamb waves is only possible under certain conditions due to their dispersive nature. [14][15][16]19,[21][22][23] Recently, some studies focus on using the effect of second-harmonic generation by the primary Lamb wave propagation to assess the early stage of damages in platelike structures.…”

“…[14][15][16]19,[21][22][23] Recently, some studies focus on using the effect of second-harmonic generation by the primary Lamb wave propagation to assess the early stage of damages in platelike structures. 17,18,20,[24][25][26] However, up to now, little work has been done on the relationship between the nonlinear Lamb waves and the microstructure evolutions in the damaged materials, such as dislocations, second phase precipitates, and micro-voids, even though it is of significance for a quantitative assessment of the damaged materials.…”

Creep damage characterization using nonlinear ultrasonic guided wave method: A mesoscale model

“…Given a line source parallel to the ox axis, within second-order perturbation, the analytical solution of the cumulative secondharmonic of Lamb waves for Eq. (1) can be derived by the modal analysis method of waveguide excitation as 14,18,19 …”

“…0021-8979/2014/115(4)/044914/11/$30.00 V C 2014 AIP Publishing LLC 115, 044914-1 potential advantage of using nonlinear Lamb waves to track creep damage is that they are capable of propagating long distances, thus making them an ideal candidate to interrogate large plate and shell structures for detecting and evaluating their early creep damages, including dislocation motions, precipitates variations, formation of micro-voids, multipoles, and micro-cracks. [14][15][16][17][18][19][20][21][22][23][24][25] In the past years, some theoretical and experimental studies of nonlinear Lamb waves have been reported. It is found that the generation of cumulative higher harmonics in Lamb waves is only possible under certain conditions.…”

“…It is found that the generation of cumulative higher harmonics in Lamb waves is only possible under certain conditions. [14][15][16]18,19,22 In order to perform a quantitative assessment or residual life prediction of the creep damaged components using the nonlinearity effect of ultrasonic guided wave, it is essential to understand the relationship between the nonlinear Lamb waves and the microstructure evolutions in the damaged materials, such as dislocations, second phase precipitates, and micro-voids.…”