Interaction of torsional and longitudinal guided waves in weakly nonlinear circular cylinders

Liu, Yang; Khajeh, Ehsan; Lissenden, Cliff J.; Rose, Joseph L.

doi:10.1121/1.4795806

Cited by 44 publications

(23 citation statements)

References 29 publications

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“…Second-harmonic generation from axis-symmetric torsional and longitudinal modes was analyzed in Ref. 34. Recently, higher order mode interactions in pipes were studied 35,36 where harmonic generation from flexural modes was analyzed as well.…”

Section: Nonlinear Guided Waves In Other Waveguidesmentioning

confidence: 99%

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

2015

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Abstract. 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. 1 Introduction Nonlinear ultrasonic nondestructive evaluation uses interrogation signals at frequencies other than the excitation frequency to detect changes in structural integrity and characterize degradation of materials. Nonlinear ultrasonic methodologies provide improved sensitivity to damage and the ability to identify incipient damage relative to linear methods. In general, linear ultrasonic methods provide good sensitivity to macroscale damage such as long fatigue cracks. However, in many cases, once damage appears at the macroscale, the remaining life is short, severely limiting maintenance decisions. Thus, characterization of incipient damage could facilitate a paradigm shift in operations of structural systems from schedule-based to condition-based maintenance that would ultimately enhance safety and reduce life cycle costs. Nonlinear ultrasonics is a broad discipline 1,2 which encompasses many specialized techniques reliant upon nonlinear material behavior to detect and/or characterize incipient damage. Some of these include nonlinear resonant ultrasound spectroscopy, 3 nonlinear elastic wave spectroscopy, 4-6 and second-harmonic generation.

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Section: Nonlinear Guided Waves In Other Waveguidesmentioning

confidence: 99%

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

2015

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“…Some recent findings from our research group related to higher harmonic generation are reported in [4][5][6][7][8].…”

Section: Higher Harmonic Generationmentioning

confidence: 95%

“…The use of time marching finite element analysis to simulate higher harmonic generation was first used by Liu et al [5,6,9]. The plate specimen is 2 mm thick by 60.3 mm wide and is over 300 mm long as shown in Fig.…”

Section: Plastic Deformation Finite Element Analysismentioning

confidence: 99%

Influence of localized microstructure evolution on second harmonic generation of guided waves

Choi

Liu

Lissenden³

et al. 2014

AIP Conference Proceedings

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The following work is intended to utilize the potential of nonlinear guided waves to characterize incipient fatigue damage. Since fatigue crack initiation often occurs in regions where there is localized microscale damage, this difficult-toanalyze condition is investigated in simplistic terms. The third order elastic constants are taken to be a function of position in accordance with the plastic strain distribution accrued during a quasistatic tension test. Two specimen geometries are considered along with multiple average plastic strain levels. Finite element analysis is employed to simulate generation of the s2 secondary Lamb mode from the S1 primary Lamb mode in al aluminum plate. The results indicate that even though the S1/s2 mode pair is synchronized and has positive power flux, the second harmonic wave mode does not accumulate linearly with propagation distance due to the inhomogeneous nature of the plate.

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“…They found that the dislocation contribution to third harmonics is 10 or more times larger than that of the lattice contribution, which makes third harmonics more suitable to study dislocation dynamics than second harmonics. The third order harmonic generation in a waveguide has been observed experimentally and numerically in previous studies [5,15], however it is not until recently that Liu et al [16] gave the mathematical formulation for the third harmonic generation due to mode interactions in a plate with cubic nonlinearity. A brief summary of key parts of the derivation is given below.…”

Section: Cumulative Third Harmonic Generationmentioning

confidence: 95%

Microstructural characterization in plates using guided wave third harmonic generation

Liu

Lissenden²,

Rose³

2014

AIP Conference Proceedings

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Interaction of torsional and longitudinal guided waves in weakly nonlinear circular cylinders

Cited by 44 publications

References 29 publications

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

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

Influence of localized microstructure evolution on second harmonic generation of guided waves

Microstructural characterization in plates using guided wave third harmonic generation

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