Frequency Dependence of Second-Harmonic Generation in Lamb Waves

Matsuda, Naoki; Biwa, Shiro

doi:10.1007/s10921-014-0227-y

Cited by 34 publications

(15 citation statements)

References 25 publications

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“…6, while the intersection angles for the maximum amplitude deviate from the resonant angles. This trend was also presented by Matsuda and Biwa [33] regarding the frequency dependence of the second-harmonic generation of a monochromatic Rayleigh-Lamb wave. These authors showed that the second-harmonic amplitude becomes maximal for the frequency deviated from the one satisfying the phase-matching condition between the fundamental and its second-harmonic modes.…”

Section: Modal Amplitude Of Secondary Wave Fieldsupporting

confidence: 76%

“…Assuming that the displacements of secondary wave are zero at X 1´ = 0, the modal amplitude in Eq. (20) is given by making use of the orthogonality of the plate wave modes as [21,32,33,40],…”

Section: Secondary Solutionmentioning

confidence: 99%

“…For plate-like structures, which are widely used in aerospace, automotive, marine, and civil engineering, nonlinear acoustic phenomena have been extensively studied such as the higher-harmonic generation [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] and the collinear interaction [21,35,36] of guided waves, while the corresponding issue for the non-collinear interaction has rarely been addressed: Furgason and Newhouse [37] experimentally demonstrated that the non-collinear mixing of Lamb waves in a lead zirconate titanate plate could generate a third wave for certain combinations of Lamb modes. Since the behavior of non-collinear interaction in plate-like structures can be more complicated than that in bulk media due to their multimode as well as dispersive nature, in-depth theoretical investigation of this issue is important academically as well as practically to apply the non-collinear mixing method to the nondestructive evaluation of plate-like structures.…”

Section: Introductionmentioning

confidence: 99%

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Non-collinear interaction of guided elastic waves in an isotropic plate

Ishii

Biwa

Adachi

2018

Journal of Sound and Vibration

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The nonlinear wave propagation in a homogeneous and isotropic elastic plate is analyzed theoretically to investigate the non-collinear interaction of plate wave modes. In the presence of two primary plate waves (Rayleigh-Lamb or shear horizontal modes) propagating in arbitrary directions, an explicit expression for the modal amplitude of nonlinearly generated wave fields with the sum or difference frequency of the primary modes is derived by using the perturbation analysis. The modal amplitude is shown to grow in proportion with the propagation distance when the resonance condition is satisfied, i.e., when the wavevector of secondary wave coincides with the sum or difference of those of primary modes. Furthermore, the non-collinear interaction of two symmetric or two antisymmetric modes is shown to produce the secondary wave fields consisting only of the symmetric modes, while a pair of symmetric and antisymmetric primary modes is shown to produce only the antisymmetric modes. The influence of the intersection angle, the primary frequencies, and the mode combinations on the modal amplitude of secondary wave is examined for a low-frequency range where the lowest-order symmetric and antisymmetric Rayleigh-Lamb waves and the lowest-order symmetric shear horizontal wave are the only propagating modes.

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Section: Modal Amplitude Of Secondary Wave Fieldsupporting

confidence: 76%

Section: Secondary Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Non-collinear interaction of guided elastic waves in an isotropic plate

Ishii

Biwa

Adachi

2018

Journal of Sound and Vibration

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“…nonlinearities was employed 38 to study center-frequency dependence of cumulative harmonic generation in isotropic plates. Likewise, two local approaches, namely cellular automata finite element and local interaction simulation approach have been employed 39 to study second-harmonic guided wave generation in waveguides.…”

Section: Numerical Simulationsmentioning

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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“…Such oscillation phenomenon for the secondary mode has also been mentioned in references. 8,9,39,40 When the deviation is small, the modal amplitude of the second harmonic wave approaches the resonant one. This suggests that in the real experiment, when the exact resonant frequency is not certain, it is still possible to collect the cumulatively increased secondary mode within a limited propagation distance.…”

Section: A Nonlinear Guided Waves In a Platementioning

confidence: 99%

Numerical studies of nonlinear ultrasonic guided waves in uniform waveguides with arbitrary cross sections

Zuo

Zhou²,

Fan

2016

AIP Advances

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Nonlinear guided waves have been investigated widely in simple geometries, such as plates, pipe and shells, where analytical solutions have been developed. This paper extends the application of nonlinear guided waves to waveguides with arbitrary cross sections. The criteria for the existence of nonlinear guided waves were summarized based on the finite deformation theory and nonlinear material properties. Numerical models were developed for the analysis of nonlinear guided waves in complex geometries, including nonlinear Semi-Analytical Finite Element (SAFE) method to identify internal resonant modes in complex waveguides, and Finite Element (FE) models to simulate the nonlinear wave propagation at resonant frequencies. Two examples, an aluminum plate and a steel rectangular bar, were studied using the proposed numerical model, demonstrating the existence of nonlinear guided waves in such structures and the energy transfer from primary to secondary modes.

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Frequency Dependence of Second-Harmonic Generation in Lamb Waves

Cited by 34 publications

References 25 publications

Non-collinear interaction of guided elastic waves in an isotropic plate

Non-collinear interaction of guided elastic waves in an isotropic plate

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

Numerical studies of nonlinear ultrasonic guided waves in uniform waveguides with arbitrary cross sections

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