On selection of primary modes for generation of strong internally resonant second harmonics in plate
TL;DR: In this article, the selection of primary shear-horizontal (SH) and Rayleigh-Lamb (RL) ultrasonic wave modes that generate cumulative second harmonics in homogeneous isotropic plates is analyzed by theoretical modeling.
About: This article is published in Journal of Sound and Vibration.The article was published on 2013-09-16. It has received 106 citations till now. The article focuses on the topics: Group velocity & Harmonics.
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TL;DR: In this paper, the authors review the recent advances in the theory of nonlinear guided waves, as well as the numerical simulations and experiments that demonstrate their utility, including the application of higher harmonic generation of ultrasonic guided wave modes for nondestructive evaluation.
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.
107 citations
TL;DR: In this paper, the authors extended the use of temporal signal processing to the realm of nonlinear Lamb waves, so as to reap the high sensitivity of Lamb wave to small-scale damage (e.g., fatigue cracks), and the efficacy of temporal signals processing in locating damage.
96 citations
TL;DR: In this article, a generalized approach is presented to analyze the nature of guided wave mode interactions in isotropic weakly nonlinear elastic plates, which facilitates systematic analysis of mode interaction in general and that of higher harmonic generation in particular.
Abstract: 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.
83 citations
TL;DR: Harmonic generation from non-cumulative fundamental symmetric and antisymmetric modes in plate is studied from a numerical standpoint and the phenomenon of mode-interaction to generate sum and difference frequencies is demonstrated.
78 citations
TL;DR: In this article, a nonlinear S0 mode Lamb wave at low frequency range satisfying approximate phase velocity matching is proposed for the purpose of overcoming the limitations of non-zero power flux criteria.
Abstract: Most previous studies on nonlinear Lamb waves are conducted using mode pairs that satisfying strict phase velocity matching and non-zero power flux criteria. However, there are some limitations in existence. First, strict phase velocity matching is not existed in the whole frequency bandwidth; Second, excited center frequency is not always exactly equal to the true phase-velocity-matching frequency; Third, mode pairs are isolated and quite limited in number; Fourth, exciting a single desired primary mode is extremely difficult in practice and the received signal is quite difficult to process and interpret. And few attention has been paid to solving these shortcomings. In this paper, nonlinear S0 mode Lamb waves at low-frequency range satisfying approximate phase velocity matching is proposed for the purpose of overcoming these limitations. In analytical studies, the secondary amplitudes with the propagation distance considering the fundamental frequency, the maximum cumulative propagation distance (MCPD) with the fundamental frequency and the maximum linear cumulative propagation distance (MLCPD) using linear regression analysis are investigated. Based on analytical results, approximate phase velocity matching is quantitatively characterized as the relative phase velocity deviation less than a threshold value of 1%. Numerical studies are also conducted using tone burst as the excitation signal. The influences of center frequency and frequency bandwidth on the secondary amplitudes and MCPD are investigated. S1–S2 mode with the fundamental frequency at 1.8 MHz, the primary S0 mode at the center frequencies of 100 and 200 kHz are used respectively to calculate the ratios of nonlinear parameter of Al 6061-T6 to Al 7075-T651. The close agreement of the computed ratios to the actual value verifies the effectiveness of nonlinear S0 mode Lamb waves satisfying approximate phase velocity matching for characterizing the material nonlinearity. Moreover, the ratios derived from the primary and secondary horizontal displacements generated from nonlinear S0 mode Lamb waves are closest to the real value, which indicates that using horizontal displacements is more suitable for detecting evenly distributed microstructural changes in large thin plate-like structure. Successful application to evaluating material at different levels of evenly distributed fatigue damage is also numerically conducted.
76 citations
Cites background from "On selection of primary modes for g..."
...Recently, Liu et al [44, 45] has extended the nonlinear Lamb waves to hollow circular cylinders....
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...These scholars include Deng [26, 27], De Lima and Hamilton [28], Chillara and Lissenden [29], Müller [30], Matsuda and Biwa [31], Matlack [32], Liu [33] and so on, and their considerable contributions put forward the development of nonlinear guided waves....
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References
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"On selection of primary modes for g..." refers background in this paper
...The equation of motion is more naturally written in terms of the first Piola–Kirchhoff stress, T0, than the second Piola– Kirchhoff stress [21]....
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TL;DR: In this article, the theory of elasticity was introduced and basic formulas and concepts in complex variables in the theory and application of wave propagation were discussed. But the authors did not consider the effects of wave scattering on the wave propagation experiments.
Abstract: Preface 1. Introduction 2. Dispersion principles 3. Unbounded isotropic and anisotropic media 4. Reflection and refraction 5. Oblique incidence 6. Wave scattering 7. Surface and subsurface waves 8. Waves in plates 9. Interface waves 10. Layer on a half space 11. Waves in rods 12. Waves in hollow cylinders 13. Guided waves in multiple layers 14. Source influence 15. Horizontal shear 16. Waves in an anisotropic layer 17. Elastic constant determination 18. Waves in viscoelastic media 19. Stress influence 20. Boundary element methods Bibliography Appendices A. Ultrasonic nondestructive testing principles, analysis and display technology B. Basic formulas and concepts in the theory of elasticity C. Basic formulas in complex variables D. Schlieren imaging and dynamic photoelasticity E. Key wave propagation experiments Index.
2,570 citations
Additional excerpts
...Guided wave solutions (see also [23])...
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