Pochhammer–Chree waves: polarization of the axially symmetric modes

Ilyashenko, A. V.; Кузнецов, С. В.

doi:10.1007/s00419-018-1377-7

Cited by 46 publications

(6 citation statements)

References 23 publications

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“…Now, assuming that (3.9) takes place, Eq. (3.8) 1 yields the following equation 10) which satisfies at some specific values of the radius R independently of 0  . Thus, the case (3.9) at 0  does not lead to any meaningful dispersion relation.…”

Section: CC Phase Velocities Equation Section (Next)mentioning

confidence: 99%

On degeneracy of dispersive waves at the bulk wave velocities

Ilyashenko

Кузнецов

2019

E3S Web Conf.

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Section: CC Phase Velocities Equation Section (Next)mentioning

confidence: 99%

On degeneracy of dispersive waves at the bulk wave velocities

Ilyashenko

Кузнецов

2019

E3S Web Conf.

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“…17,18 It is also known that the zone in the vicinity of ZGV is prone to large oscillations, which may cause the plate "ringing;" see. [19][20][21][22][23][24] Group slowness, group velocity, and zero group velocity. Following, 25 introduce slowness associated with phase and group velocities…”

Section: Introductionmentioning

confidence: 99%

“…17,18 It is also known that the zone in the vicinity of ZGV is prone to large oscillations, which may cause the plate “ringing;” see. 19–24…”

Section: Introductionmentioning

confidence: 99%

On infinite group velocity in composite plates

Kuznetsov

2023

Jnl of Sandwich Structures & Materials

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The analytical and geometrical conditions for the possible appearance of the infinite group velocity (IGV) points belonging to the dispersion curves of Lamb waves propagating in traction-free plates are studied by a combined method comprising Cauchy sextic formalism and the exponential fundamental matrix method. According to the obtained geometrical condition, the IGV corresponds to the coincidence of a tangent line to any of the dispersion curves with a straight line passing through the origin. The developed technique is demonstrated by applying to the analysis of Lamb wave dispersion in three-layered plates with a soft inner core.

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“…In previous studies, the Pochhammer–Chree wave is described as a harmonic wave that propagates in a cylindrical rod (Pochhammer, 1876; Chree, 1886). The exact solution of Pochhammer–Chree waves was analysed by Ilyashenko and Kuznetsov (2018), which gives different dispersive modes, and the high‐frequency asymptote is related to the interfacial Stoneley wave. The criteria for the existence of the Stoneley wave in a stratified media appears at the high‐end frequency limit of the Lamb wave (Kuznetsov 2020).…”

Section: Introductionmentioning

confidence: 99%

Fracture analysis using Stoneley waves in a coalbed methane reservoir

Banerjee

Chatterjee

2021

Near Surface Geophysics

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The production of coalbed methane gas depends upon various factors such as permeability, gas content, gas saturation and seam thickness. The low permeability in coal is a constraint in the gas extraction process. However, the presence of natural fractures and cleats in coal increases the permeability; therefore, its identification is necessary to establish the prospectivity. Hence, a methodology is used to process the Stoneley waveform in the Bokaro coalfield located in India to obtain slowness magnitude from the semblance analysis. The separation of directly transmitted and reflected Stoneley waves determines the reflection coefficient and attenuation, and its analysis emphasizes the presence of fractures. In coal seams, the average reflection coefficient ranges from 0.42 to 2.44 and attenuation ranges from 0.2 dB to 12.68 dB. The Stoneley slowness versus frequency plot shows a constant slowness with increasing frequency in the non-fractured seams, whereas a dispersive trend is observed in the fractured seams. Fractures are also distinguished from the cross-plot of compressional/shear versus Stoneley velocity. The observation of higher reflection coefficient, attenuation and slowness-frequency dispersion in coal seams indicates extensive fractures/cleats that corroborate with the resistivity image log correlation. Thus, the study helps to distinguish between fractured and non-fractured coal seams from the integrated approach of reflection coefficient, attenuation and dispersion analysis of Stoneley waves supported by the identification of fractures from resistivity image log for optimization in coalbed methane production in the development phase.

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Pochhammer–Chree waves: polarization of the axially symmetric modes

Cited by 46 publications

References 23 publications

On degeneracy of dispersive waves at the bulk wave velocities

On degeneracy of dispersive waves at the bulk wave velocities

On infinite group velocity in composite plates

Fracture analysis using Stoneley waves in a coalbed methane reservoir

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