@article{f0686a7b2cb647dfb430573f4dae6b8e,
title = "Experimental characterization of efficient second harmonic generation of Lamb wave modes in a nonlinear elastic isotropic plate",
abstract = "This research experimentally characterizes the efficiency of Lamb wave mode pairs to generate the cumulative second harmonic in an undamaged aluminum plate. Previous research developed the theoretical framework for the characteristics of second harmonic generation of Lamb waves in nonlinear elastic plates, and identified five mode types where the amplitude of the measured second harmonic should increase linearly with ultrasonic wave propagation distance. The current research considers one of these five mode types, Lamb wave mode pairs at the longitudinal velocity, and experimentally confirms the theoretically predicted ratios of the rate of accumulation of the second harmonic amplitude versus propagation distance for two different Lamb wave mode pairs. By comparing these rates of accumulation, these experimental results are used to characterize the measurement efficiency of the mode pairs under consideration.",
author = "Matlack, {Kathryn H.} and Kim, {Jin Yeon} and Jacobs, {Laurence J.} and Jianmin Qu",
note = "Funding Information: This work was partially supported by the National Science Foundation through a Graduate Research Fellowship to Kathryn Matlack and by the Air Force Office of Scientific Research under Contract No. FA9550-08-1-0241. Table I. Summary of Lamb wave mode pair parameters. The normalized displacement of the primary mode at the surface of the plate, h , is given in terms of in-plane displacement, u ¯ z ( h ) , and out-of-plane (normal) displacement, u ¯ y ( h ) (these displacements are normalized by the displacement of the primary wave in mode pair s1-s2; displacements are calculated with the software DISPERSE ). Mode pair Ref. f d (MHz mm) c p h (m/s) c g (m/s) u ¯ y ( h ) u ¯ z ( h ) r s s1-s2 L 1 3.603 6320 4326 0 1.000 3.76 s2-s4 L 2 7.206 6320 4326 0 0.499 15.05 a2-s4 C 1 5.095 8057 2000 0 0.705 2.49 FIG. 1. Symmetric and antisymmetric Lamb wave modes in terms of (a) phase velocity and (b) group velocity, showing experimental mode pairs (superscripts on mode pair designations distinguish between primary and secondary mode). FIG. 2. Theoretical comparison of rate of accumulation of the second harmonic of selected mode pairs. FIG. 3. Time slices of s2-s4 received signal at a propagation distance of z = 35 cm at the first and second harmonic frequency. FIG. 4. Measured primary wave amplitude of s1-s2 mode pair and the diffraction model for a point source, a circular source, and a line source/receiver. FIG. 5. Comparison of experimental β ′ for s1-s2 and s2-s4 mode pairs. The ratio of the measured rate of accumulation is 4.23. ",
year = "2011",
month = jan,
day = "1",
doi = "10.1063/1.3527959",
language = "English (US)",
volume = "109",
journal = "Journal of Applied Physics",
issn = "0021-8979",
publisher = "American Institute of Physics",
number = "1",
}