Interest in using the higher harmonic generation of ultrasonic guided wave modes for nondestructive evaluation continues to grow tremendously as the understanding of nonlinear guided wave propagation has enabled further analysis. The combination of the attractive properties of guided waves with the attractive properties of higher harmonic generation provides a very unique potential for characterization of incipient damage, particularly in plate and shell structures. Guided waves can propagate relatively long distances, provide access to hidden structural components, have various displacement polarizations, and provide many opportunities for mode conversions due to their multimode character. Moreover, higher harmonic generation is sensitive to changing aspects of the microstructures such as to the dislocation density, precipitates, inclusions, and voids. We review the recent advances in the theory of nonlinear guided waves, as well as the numerical simulations and experiments that demonstrate their utility.

https://www.spiedigitallibrary.org/journals/optical-engineering/volume-55/issue-1/011002/Review-of-nonlinear-ultrasonic-guided-wave-nondestructive-evaluation--theory/10.1117/1.OE.55.1.011002.pdf

Review of nonlinear ultrasonic guided wave nondestructive evaluation: theory, numerics, and experiments

https://digital.library.adelaide.edu.au/dspace/bitstream/2440/111027/2/hdl_111027.pdf

Second harmonic generation at fatigue cracks by low-frequency Lamb waves: experimental and numerical studies

On selection of primary modes for generation of strong internally resonant second harmonics in plate

Ultrasonic waves for materials evaluation in fatigue, thermal and corrosion damage: A review

Locating fatigue damage using temporal signal features of nonlinear Lamb waves

A generalized approach is presented to analyze the nature of guided wave mode interactions in isotropic weakly nonlinear elastic plates. The problem formulation is carried out in terms of the displacement gradient, which facilitates systematic analysis of mode interactions in general and that of higher harmonic generation in particular. Only cumulative harmonics are analyzed; these (1) have nonzero power flow and (2) are phase matched. Results indicate that the interaction of Rayleigh-Lamb modes of the same nature (symmetric or antisymmetric) can generate only cumulative harmonics that are symmetric modes, while the interaction between modes of opposite nature can generate only cumulative harmonics that are antisymmetric modes. A methodology for assessing cumulative higher harmonic generation (e.g., the third harmonic) is also proposed.

Interaction of guided wave modes in isotropic weakly nonlinear elastic plates: Higher harmonic generation

Nonlinear guided waves in plates: a numerical perspective.

The third order harmonic generation (third harmonics as well as cubic sum and difference harmonics) due to the cubic interaction of two collimated elastic waves in a homogeneous, isotropic, weakly nonlinear plate is investigated by using a fourth order expansion of strain energy density to formulate the nonlinear boundary problems. Waves with both shear horizontal (SH) and Rayleigh Lamb (RL) nature are considered as primary or tertiary wave fields. The non-zero power flux condition is evaluated using characteristic parity matrices of the cubic nonlinear forcing terms and third order harmonic mode shapes. Results indicate that waves with either SH or RL nature receive power flux from a specific pattern of primary mode interaction. Further analytical evaluation of the synchronism condition enables identification of primary SH and RL modes that are able to generate cumulative third harmonics. The primary SH modes are shown to be holo-internal-resonant with third harmonic SH fields. This simply means that all points on the primary dispersion curves are internally resonant with third harmonics, which is not the case for second harmonics. Such flexibility will be advantageous for laboratory and field measurements.

Vamshi Krishna Chillara

Papers

Review of nonlinear ultrasonic guided wave nondestructive evaluation: theory, numerics, and experiments

On selection of primary modes for generation of strong internally resonant second harmonics in plate

Interaction of guided wave modes in isotropic weakly nonlinear elastic plates: Higher harmonic generation

Nonlinear guided waves in plates: a numerical perspective.

Third harmonic shear horizontal and Rayleigh Lamb waves in weakly nonlinear plates