Possible second-order nonlinear interactions of plane waves in an elastic solid

Korneev, Valeri; Demčenko, Andriejus

doi:10.1121/1.4861241

Cited by 64 publications

(51 citation statements)

References 26 publications

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“…The reason for this may come from the absence of quadratic nonlinearity induced by a shear strain. 1 Laboratory rock experiments include nonlinear effects on shear wave propagation such as shear wave splitting under uni-axial stress 29 and interaction between compressional and shear waves, [30][31][32][33] but this does not include a shear strain component in the origin of the nonlinearity. The choice of a shear wave pump in this paper aims to consider a realistic pump strain field in a subsurface experiment, which includes shear components.…”

Section: Introductionmentioning

confidence: 99%

Characterizing the nonlinear interaction of S- and P-waves in a rock sample

Gallot

Malcolm

Szabo

et al. 2015

Journal of Applied Physics

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The nonlinear elastic response of rocks is known to be caused by the rocks' microstructure, particularly cracks and fluids. This paper presents a method for characterizing the nonlinearity of rocks in a laboratory scale experiment with a unique configuration. This configuration has been designed to open up the possibility of using the nonlinear characterization of rocks as an imaging tool in the field. In our experiment, we study the nonlinear interaction of two traveling waves: a low-amplitude 500 kHz P-wave probe and a high-amplitude 50 kHz S-wave pump in a room-dry 15 Â 15 Â 3 cm slab of Berea sandstone. Changes in the arrival time of the P-wave probe as it passes through the perturbation created by the traveling S-wave pump were recorded. Waveforms were time gated to simulate a semi-infinite medium. The shear wave phase relative to the P-wave probe signal was varied with resultant changes in the P-wave probe arrival time of up to 100 ns, corresponding to a change in elastic properties of 0.2%. In order to estimate the strain in our sample, we also measured the particle velocity at the sample surface to scale a finite difference linear elastic simulation to estimate the complex strain field in the sample, on the order of 10 À6 , induced by the S-wave pump. We derived a fourth order elastic model to relate the changes in elasticity to the pump strain components. We recover quadratic and cubic nonlinear parameters:b ¼ À872 and d ¼ À1:1 Â 10 10 , respectively, at room-temperature and when particle motions of the pump and probe waves are aligned. Temperature fluctuations are correlated to changes in the recovered values ofb andd, and we find that the nonlinear parameter changes when the particle motions are orthogonal. No evidence of slow dynamics was seen in our measurements. The same experimental configuration, when applied to Lucite and aluminum, produced no measurable nonlinear effects. In summary, a method of selectively determining the local nonlinear characteristics of rock quantitatively has been demonstrated using traveling sound waves. V C 2015 AIP Publishing LLC.

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Section: Introductionmentioning

confidence: 99%

Characterizing the nonlinear interaction of S- and P-waves in a rock sample

Gallot

Malcolm

Szabo

et al. 2015

Journal of Applied Physics

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“…The non-collinear interaction has been studied for bulk waves in isotropic elastic media theoretically [4][5][6][7][8] as well as numerically [9,10], leading to the derivation of the so-called resonance condition for the occurrence of third waves, i.e., the ratio of driving frequencies, the angle of intersection, and the combination of the incident and third wave modes. The third waves generated by the non-collinear interaction were experimentally observed by Rollins et al [11], and the influence of applied stress on the generation behavior of third wave was investigated by Hirao et al [12].…”

Section: Introductionmentioning

confidence: 99%

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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“…Under phase matching or "resonance" conditions, the periodicity of the interference pattern produced by the two incident shear waves matches the wavelength of the longitudinal wave so that cumulative mixing occurs over the whole interaction volume [15][16][17][18]. The optimal interaction angle φ = θ 1 + θ 2 between the two shear waves can be calculated from…”

Section: Theorymentioning

confidence: 99%