On degeneracy of dispersive waves at the bulk wave velocities

Degeneracy of the linear dispersion wave equation at the phase velocities coinciding with the bulk wave velocities is observed and analysed. Spectral analysis of Pochhammer – Chree equation is performed. The corrected analytical solutions for components of the displacement fields are constructed, accounting degeneracy of the secular equations and the corresponding solutions.

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Stress Field of Semi-Infinite Interface Crack Tip of Double Dissimilar Orthotropic Composite Materials

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.97-101.1223 ◽

2010 ◽

Vol 97-101 ◽

pp. 1223-1226

Author(s):

Jun Lin Li ◽

Shao Qin Zhang

Keyword(s):

Composite Material ◽

Composite Materials ◽

Interface Crack ◽

Interfacial Crack ◽

Crack Tip ◽

Stress Fields ◽

Displacement Fields ◽

Orthotropic Composite ◽

Stress Functions ◽

Secular Equations

The problem of orthotropic composite materials semi-infinite interfacial crack was studied, by constructing new stress functions and employing the method of composite material complex. In the case that the secular equations’ discriminates the and theoretical solutions to the stress fields and the displacement fields near semi-infinite interface crack tip without oscillation and inter-embedding between the interfaces of the crack are obtained, a comparison with finite element example was done to verify the correction of theoretical solution.

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New Analytical Solutions of Fractional Symmetric Regularized-Long-Wave Equation

Revista Mexicana de Física ◽

10.31349/revmexfis.66.297 ◽

2020 ◽

Vol 66 (3 May-Jun) ◽

pp. 297

Author(s):

Mehmet Senol

Keyword(s):

Wave Equation ◽

Analytical Solutions ◽

Fractional Derivatives ◽

Algebraic Method ◽

Symbolic Calculation ◽

Solution Sets ◽

Flow Models ◽

Long Wave ◽

Regularized Long Wave Equation ◽

Fractional Differential

In this study, new extended direct algebraic method is successfully implemented to acquire new exact wave solution sets for symmetric regularized-long-wave (SRLW) equation which arise in long water flow models. By the help of Mathematica symbolic calculation package, the method produced a great number of analytical solutions. We also presented a few graphical illustrations for some surfaces. The fractional derivatives are considered in the conformable sense. All of the solutions were checked by substitution to ensure the reliability of the method. Obtained results confirm that the method is straightforward, powerful and effective method to attain exact solutions for nonlinear fractional differential equations. Therefore, the method is a good candidate to take part in the existing literature.

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Measurement of mantle wave velocities and inversion for lateral heterogeneity and anisotropy: 1. Analysis of Great Circle Phase Velocities

Journal of Geophysical Research Atmospheres ◽

10.1029/jb088ib12p10267 ◽

1983 ◽

Vol 88 (B12) ◽

pp. 10267-10283 ◽

Cited By ~ 77

Author(s):

Ichiro Nakanishi ◽

Don L. Anderson

Keyword(s):

Great Circle ◽

Lateral Heterogeneity ◽

Wave Velocities ◽

Phase Velocities ◽

And Inversion

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Nonlinear wave equation with intrinsic wave particle dualism

Canadian Journal of Physics ◽

10.1139/p76-162 ◽

1976 ◽

Vol 54 (13) ◽

pp. 1383-1390 ◽

Cited By ~ 2

Author(s):

J. J. Klein

Keyword(s):

Wave Equation ◽

Nonlinear Wave ◽

Nonlinear Wave Equation ◽

Gordon Equation ◽

Classical Mechanics ◽

Carrier Wave ◽

Sine Gordon Equation ◽

Wave Speeds ◽

Phase Velocities ◽

Group And Phase Velocities

A nonlinear wave equation[Formula: see text]derived from the sine–Gordon equation is shown to possess a variety of solutions, the most interesting of which is a solution that describes a wave packet travelling with velocity uc modulating a carrier wave travelling with velocity uc. The envelop and carrier wave speeds agree precisely with the group and phase velocities found by de Broglie for matter waves. No spreading is exhibited by the soliton, so that it behaves exactly like a particle in classical mechanics. Moreover, the classically computed energy E of the disturbance turns out to be exactly equal to the frequency ω of the carrier wave, so that the Planck relation [Formula: see text] is automatically satisfied without postulating a particle–wave dualism.

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Identification of the Model of Nonlinear Elasticity in Dynamic Experiments

International Journal of Applied Mechanics ◽

10.1142/s1758825121500253 ◽

2021 ◽

pp. 2150025

Author(s):

Marina Sokolova ◽

Yuri Astapov ◽

Dmitrii Khristich

Keyword(s):

Deformable Body ◽

Polyamide 6 ◽

Preliminary Deformation ◽

Transverse Waves ◽

Wave Velocities ◽

Phase Velocities ◽

Dynamic Methods ◽

Dynamic Experiments ◽

Effective Phase ◽

Nonlinearly Elastic

Dynamic methods for identifying a model of a nonlinearly elastic deformable body are considered. By the effective phase velocities of longitudinal and transverse waves propagating along and across the axis of the compressed bar, it is possible to determine five elastic constants of the second and third orders included in the model relations. Calculation formulae are obtained and an example of determining the dependence of phase velocities on the preliminary deformation for polyamide 6 is given. The influence of preliminary deformations on polar diagrams of wave velocities is investigated.

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Stress wave velocity measured in intact pig lungs with cross-spectral analysis

Journal of Applied Physiology ◽

10.1152/jappl.1994.76.2.565 ◽

1994 ◽

Vol 76 (2) ◽

pp. 565-571 ◽

Cited By ~ 12

Author(s):

M. Jahed ◽

S. J. Lai-Fook

Keyword(s):

Spectral Analysis ◽

Stress Wave ◽

Intratracheal Instillation ◽

Weight Ratio ◽

Transpulmonary Pressure ◽

Dry Weight ◽

Stress Waves ◽

Wave Velocities ◽

Esophageal Balloon

In anesthetized pigs (25–40 kg), we generated stress waves in the lung by rapid deflation of an esophageal balloon. The source distortion was measured by an accelerometer (1 g wt) bonded to the balloon. Stress waves were detected by three accelerometers bonded to intercostal muscle and to the skin near midchest. The distance between the source and chest receivers were measured radiographically. Cross-spectral analysis was used to calculate transit times. We measured stress wave velocities at airway pressures of 0 (functional residual capacity) and 25 cmH2O. Transpulmonary pressure (Ptp) was measured by an esophageal balloon. In vivo, stress wave velocities increased from 291 +/- 117 (SD) cm/s at 3.0 +/- 0.9 cmH2O Ptp to 573 +/- 73 cm/s at 13.8 +/- 3.5 cmH2O Ptp (n = 6). These velocities agreed with longitudinal wave velocities measured in isolated sheep lungs and predictions based on the elastic moduli of lung parenchyma. Post-mortem edema was induced by intratracheal instillation of 200 ml of saline, resulting in a wet-to-dry weight ratio of 7.7 +/- 1.4 (n = 5). At 15 cmH2O Ptp, stress wave velocities decreased from 565 +/- 155 cm/s before edema to 445 +/- 130 cm/s after edema. This decrease correlated well with predictions based on the increased lung density, as dictated by elasticity theory.

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