Second-harmonic generation of two-dimensional elastic wave propagation in an infinite layered structure with nonlinear spring-type interfaces

Ishii, Yosuke; Biwa, Shiro; Adachi, Tadaharu

doi:10.1016/j.wavemoti.2020.102569

Cited by 9 publications

(3 citation statements)

References 47 publications

(123 reference statements)

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“…It can also be obtained as a limiting case of a thin nonlinear elastic interphase layer, as discussed by An et al 40 and Zhang et al 41 It has been used in the analysis of the second-harmonic generation at contacting interfaces for normally incident waves 28,30 and for more general situations. 36,42 Similar models can be found in other works 27,29,31 on the contact acoustic nonlinearity. For the sake of brevity, the nonlinear effects of the closed crack are solely represented by the term by 2 ðx 1 ; tÞ 2 on the right-hand side of Eq.…”

Section: Formulation Of the Problemsupporting

confidence: 73%

Second-harmonic generation of the lowest-order antisymmetric Lamb wave at a closed parallel crack

Biwa

Mori

2020

The Journal of the Acoustical Society of America

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The second-harmonic generation of the fundamental antisymmetric Lamb wave at a closed parallel crack in an elastic plate is studied by numerical analysis. The closed crack is modeled as a spring-type interface with quadratic nonlinearity. Based on a perturbation method, the problem of nonlinear Lamb wave scattering is decomposed into two linearized problems, i.e., for the linear reflection/transmission of the incident Lamb wave at the crack and for the generation/radiation of the second-harmonic Lamb waves due to the contact nonlinearity. The reduced problems are solved by the finite element method in the frequency domain. Numerical results demonstrate significant effects of the crack resonance on the linear and nonlinear Lamb wave scattering responses, which appear as sharp peaks/dips in the reflection/transmission spectra and enhanced second-harmonic amplitudes at some frequencies. Two simple frequency selection rules are established which explain the enhanced generation of the second-harmonic Lamb waves. The time-domain analysis is also carried out to supplement the frequency-domain analysis, which confirms that the incident Lamb wave interacts with the crack at some specific frequencies in its bandwidth in a selective manner and enhances the generation of the second-harmonic components. V

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Section: Formulation Of the Problemsupporting

confidence: 73%

Second-harmonic generation of the lowest-order antisymmetric Lamb wave at a closed parallel crack

Biwa

Mori

2020

The Journal of the Acoustical Society of America

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“…By generating higher harmonics in periodic systems, a fraction of the energy is transferred to frequencies that are multiples of the excitation frequency. [ 161,163,165–186 ] Such an energy transfer enables many important properties, such as modal interaction, [ 165,171,179 ] intermodal hopping, [ 170 ] self‐switching functionality selection capabilities, [ 169 ] bandgap tunability, [ 174 ] and wave reflection manipulation. [ 175,176 ] Recently, some of the efforts have been devoted to breaking the reciprocity to create phonon diodes by generating higher harmonics.…”

Section: Size Effect On Phononic Crystals and Acoustic Metamaterialsmentioning

confidence: 99%

Phonon Engineering of Micro‐ and Nanophononic Crystals and Acoustic Metamaterials: A Review

2022

Small Science

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Figure 2. a,e) Experimental specimens of a regular Kagome lattice (a) and a topological Kagome lattice (e). b,f ) Isofrequency contours (first phaseconstant surface in the first Brillouin zone) of regular (b) and topological (f ) Kagome lattices calculated from FEA. c,g) Group velocity isofrequency contours (frequency increasing from dark red to bright yellow) highlighting symmetric or asymmetric directivity of regular (c) and topological (g) lattices. d,h) Snapshots of experimentally acquired wave fields in regular (d) and topological (h) lattices, confirming symmetric or asymmetric propagation. Colors denotes the magnitude of the scan point velocities, normalized by the largest value at the considered instants. a-h) Reproduced with permission. [40]

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“…Balvantín studied experimentally and theoretically the effect of loading and unloading cycles on the guided wave propagation parameters [29]. Ishii analyzed theoretically the two-dimensional elastic wave propagation in an infinite layered structure with non-linear interlayer interfaces for investigating the second-harmonic generation due to interfacial nonlinearity [30]. Many other works have been carried out for ultrasonic characterization of the interfacial weakness in multilayered structure [31,32].…”

Section: Introductionmentioning

confidence: 99%

Evaluating interfacial bonding quality of multilayered structure based on ultrasonic testing technology

Wang

et al. 2023

Meas. Sci. Technol.

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An ultrasonic evaluation method of interfacial bonding quality from layered structures is proposed for enhancing the testing accuracy. The ultrasonic reflection and transmission characteristic is theoretically analyzed, which focus on the different quality of the single and double bonding interface with spring-type. The reflection coefficient and transmission coefficient mathematic models, which include multiple parameters, are derived from the transfer matrix. Taking the first, second, and the double bonding interface as the research objects, respectively, two types of resonant frequencies have been presented by numerical solving the model, namely, the first type resonance frequency (RFI) and the second type resonance frequency (RFII). The results show that the interval of the RFⅠ is related to medium thickness of the maximum acoustic impedance. Similarly, the interval of the RFⅡ depends on other layers’ thickness. In addition, the transmission coefficient shows a change in different trends with the bonding interface gradually tending to rigid. When the adhesive layer thickness is sufficiently small compared with the wavelength, the reflection coefficient shows many local minima points at a certain frequencies range, the frequency of local minimum point increases with the increase of the stiffness coefficient. The experimental results are in good agreement with the numerical solution results and finite element analysis (FEA) results.

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Second-harmonic generation of two-dimensional elastic wave propagation in an infinite layered structure with nonlinear spring-type interfaces

Cited by 9 publications

References 47 publications

Second-harmonic generation of the lowest-order antisymmetric Lamb wave at a closed parallel crack

Second-harmonic generation of the lowest-order antisymmetric Lamb wave at a closed parallel crack

Phonon Engineering of Micro‐ and Nanophononic Crystals and Acoustic Metamaterials: A Review

Evaluating interfacial bonding quality of multilayered structure based on ultrasonic testing technology

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