On elastic waves in a wedge

Zavorokhin, G. L.; Nazarov, Alexander I.

doi:10.1007/s10958-011-0380-0

Cited by 17 publications

(6 citation statements)

References 4 publications

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“…When inserting (28) and (29) in (27), multiplying both sides of this equation by * x from 0 to infinity, performing two integrations by parts, thereby obeying the traction-free boundary conditions at the surface, the following infinite set of differential equations is obtained:…”

Section: Rayleigh Wavesmentioning

confidence: 99%

“…In isotropic elastic wedges, acoustic modes may be characterized as either even or odd, depending on their behavior with respect to the reflection at the wedge's midplane (x 1 = x 2 ). For opening angles smaller than 90° and Poisson ratios in the range of most materials of practical use, only odd wedge waves (anti-symmetric flexural modes, ASF modes) exist [27]. Unlike Rayleigh waves, ASF modes do not resonantly generate even harmonics [28].…”

Section: Acoustic Wedge Wavesmentioning

confidence: 99%

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Nonlinear effects of micro-cracks on acoustic surface and wedge waves

Rjelka

Pupyrev

Koehler

et al. 2018

Low Temperature Physics

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Micro-cracks give rise to non-analytic behavior of the stress-strain relation. For the case of a homogeneous spatial distribution of aligned flat micro-cracks, the influence of this property of the stress-strain relation on harmonic generation is analyzed for Rayleigh waves and for acoustic wedge waves with the help of a simple micromechanical model adopted from the literature. For the efficiencies of harmonic generation of these guided waves, explicit expressions are derived in terms of the corresponding linear wave fields. The initial growth rates of the second harmonic, i.e., the acoustic nonlinearity parameter, has been evaluated numerically for steel as matrix material. The growth rate of the second harmonic of Rayleigh waves has also been determined for microcrack distributions with random orientation, using a model expression for the strain energy in terms of strain invariants known in a geophysical context.

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Section: Rayleigh Wavesmentioning

confidence: 99%

Section: Acoustic Wedge Wavesmentioning

confidence: 99%

Nonlinear effects of micro-cracks on acoustic surface and wedge waves

Rjelka

Pupyrev

Koehler

et al. 2018

Low Temperature Physics

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“…The first rigor proof of existence of the wedge wave was obtained in the pioneering paper [9] by variational method for openings less then π 2 . Then the idea of [9] was developed in [39] and [30] where the range of aperture angles was enlarged. Further applications of this idea can be found in [3] and [31].…”

Section: Introduction Statement Of the Problemmentioning

confidence: 99%

“…, and the symmetric modes 4) Numerical simulations in [21], [35] predict the existence of symmetric modes (4) for obtuse wedges. The existence of such modes was proved rigorously in [39] and [30] for certain values of the Poisson ratio σ = λ 2(λ+µ) and some range of wedge openings that are far from π. Now we formulate our main result.…”

Section: Introduction Statement Of the Problemmentioning

confidence: 99%

On symmetric wedge mode of an elastic solid

Nazarov,

Zavorokhin

2019

Preprint

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“…Two distinct vibrational modes theoretically exist for the wedge wave: breathing and wagging. The breathing mode is similar to a bellows opening and closing but is only predicted for a special range of material properties (Moss et al, ; Zavorokhin & Nazarov, ). The wagging mode is like a dog's tail, which oscillates side to side, and is the most common mode for the wedge wave.…”

Section: Introductionmentioning

confidence: 99%

Intersection Waves

2017

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Intersections in a fracture network control the connectivity of the flow paths through rock. The long near‐linear geometric nature of fractures makes them difficult to identify and characterize. We present a new type of elastic wave, an intersection wave, which travels along an intersection and is sensitive to the coupling between two orthogonal fractures that define the intersection. Group theory for C2v and C4v point groups predicts sets of propagating elastic waves confined to the fracture intersection. Along with the use of the wave equation and displacement discontinuity boundary conditions, the dispersion relationships for intersection waves are predicted. Experimental ultrasonic measurements on a nonwelded linear intersection between two orthogonal, synthetic fractures in aluminum confirm the existence of multiple modes that travel between the speed of wedge waves (sub‐Rayleigh waves) when the intersection is completely, and bulk shear waves, when the intersection is closed, as predicted by theory. Between these two limits, the intersection behaves as a nonwelded contact and yields these new intersection waves that are dispersive and sensitive to the coupling along the intersection. Intersection waves provide the foundation for new geophysical approaches for characterizing the hydraulic connectivity of fracture networks.

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On elastic waves in a wedge

Cited by 17 publications

References 4 publications

Nonlinear effects of micro-cracks on acoustic surface and wedge waves

Nonlinear effects of micro-cracks on acoustic surface and wedge waves

On symmetric wedge mode of an elastic solid

Intersection Waves

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