scholarly journals FRACTIONAL CALCULUS OF THERMOELASTIC p-WAVES REFLECTION UNDER INFLUENCE OF GRAVITY AND ELECTROMAGNETIC FIELDS

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040037 ◽  
Author(s):  
HAMMAD ALOTAIBI ◽  
S. M. ABO-DAHAB ◽  
H. R. ABDLRAHIM ◽  
A. A. KILANY
Keyword(s):  
Fractional Calculus ◽  
Function Method ◽  
Elastic Half Space ◽  
Harmonic Waves ◽  
P Waves ◽  
Reflected Waves ◽  
Gravity Fields ◽  
Fractional Exponential Function ◽  
Exponential Function Method ◽  
Incident Waves

In this paper, we discussed the longitudinal harmonic waves reflection from a solid elastic half-space with electromagnetic and gravity fields influence, considering a fractional order via fractional exponential function method. The clarifications are required for the reflection amplitudes ratios (i.e. the ratios between the reflected waves amplitude and the incident waves amplitude). The results obtained were calculated analytically and displayed by graphs to show the physical meaning of the phenomenon. A comparison has been made between the fractional and integer derivatives. The results of this paper demonstrate the rigor and effectiveness of the considered fractional technique.

Quaternion-based anisotropic inversion for flexural waves in horizontal transverse isotropic formations with unmatched sources: A synthetic example

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. A69-A74 ◽  
Author(s):  
Fuqiang Zeng ◽  
Wenzheng Yue ◽  
Chao Li
Keyword(s):  
Structural Information ◽  
Amplitude Ratio ◽  
Flexural Wave ◽  
Data Sets ◽  
Flexural Waves ◽  
P Waves ◽  
Source Type ◽  
Transverse Isotropic ◽  
Sonic Logging ◽  
Incident Waves

The anisotropy of elastic waves has been widely used to obtain structural information on formations in geosciences research. Flexural wave splitting is generally applied to evaluate anisotropy with geophysical inversion methods. Cross-dipole sonic logging has been widely used for anisotropic inversions in horizontal transverse isotropic formations. Traditional methods assume that fast and slow flexural waves are similar in shape and are not dispersive and that the radiation characteristics of the two orthogonal dipole sources are identical. The two above assumptions cannot be satisfied in field conditions. Therefore, the methods used in anisotropy inversion based on these assumptions will lead to inaccurate results. The introduction of the amplitude ratio (AR), the ratio of slow to fast flexural waves, which is not dependent on the source type, can eliminate the wave-shape assumption. Two data sets from orthogonally oriented receivers can be constructed as a quaternion array. Fast and slow flexural waves are the two main incident waves, and other arrivals such as P-waves can be taken as noise. The AR and a quaternion multiple signal classification algorithm are used to demonstrate how to improve the anisotropic inversion and avoid these assumptions. Compared with the traditional method, the new method presents better inversion results for the synthetic example with two different sources. We have determined that the inversion residual from the new objective function can be used to indicate the inversion quality.

Stress Wave Propagation in a Coated Elastic Half-Space due to Water Drop Impact

2000 ◽  
Vol 68 (2) ◽  
pp. 346-348 ◽  
Author(s):  
Hyun-Sil Kim ◽  
Jae-Seung Kim ◽  
Hyun-Ju Kang ◽  
Sang-Ryul Kim
Keyword(s):  
Wave Propagation ◽  
Half Space ◽  
Stress Wave ◽  
Coating Thickness ◽  
Water Drop ◽  
Elastic Half Space ◽  
Drop Impact ◽  
Stress Wave Propagation ◽  
Singular Behavior ◽  
Reflected Waves

Stress wave propagation in a coated elastic half-space due to water drop impact is studied by using the Cagniard-de Hoop method. The stresses have singularity at the Rayleigh wavefront whose location and singular behavior are determined from the pressure model and independent of the coating thickness, while reflected waves cause minor changes in amplitudes.

Effects of Surface Elasticity on Scattering of P Waves by an Elastic Half-Plane with a Nanosized Semi-Cylindrical Inclusion

2013 ◽  
Vol 303-306 ◽  
pp. 2661-2666
Author(s):  
Zhi Ying Ou ◽  
Cheng Liu ◽  
Xiao Wei Liu
Keyword(s):  
Surface Energy ◽  
Half Plane ◽  
Surface Effect ◽  
Surface Elasticity ◽  
Expansion Method ◽  
Cylindrical Inclusion ◽  
P Waves ◽  
Wave Function Expansion Method ◽  
Plane P Waves ◽  
Incident Waves

The scattering of plane P waves by a nanosized semi-cylindrical inclusion embedded in an elastic half-plan has been studied in this paper. To account for the surface effect at nanoscale, the surface elasticity is also adopted. When the boundary condition at the straight edge of the half-plane is traction free, the analytical solutions of stress fields of the half plan with semi-cylindrical inclusion are expressed by employing a wave function expansion method. The results show that surface energy has a significant effect on the scattering of plane P waves as the radius of the semi-cylindrical inclusion shrinks to nanoscale. For incident waves with different frequencies, radius of semi-cylindrical inclusion, the effects of surface energy on the dynamic stress concentration near the semi-cylindrical inclusion are discussed in detail.

Response of a plate and elastic half-space to harmonic waves

1982 ◽  
Vol 10 (2) ◽  
pp. 255-266 ◽  
Author(s):  
W. L. Whittaker ◽  
Paul Christiano
Keyword(s):  
Half Space ◽  
Elastic Half Space ◽  
Harmonic Waves

Instability of a stratified boundary layer and its coupling with internal gravity waves. Part 2. Coupling with internal gravity waves via topography

2008 ◽  
Vol 595 ◽  
pp. 409-433 ◽  
Author(s):  
XUESONG WU ◽  
JING ZHANG
Keyword(s):  
Boundary Layer ◽  
Gravity Waves ◽  
Internal Gravity Waves ◽  
Shear Instability ◽  
Acoustic Analogy ◽  
Physical Processes ◽  
Reflected Waves ◽  
Instability Modes ◽  
Viscous Shear ◽  
Incident Waves

The aim of this paper is to show that the viscous shear instability identified in Part 1 is intrinsically coupled with internal gravity waves when a localized surface topography is present within a boundary layer. The coupling involves two aspects: receptivity and radiation. The former refers to excitation of shear instability modes by gravity waves, and the latter to emission of gravity waves by instability modes. Both physical processes are studied using triple-deck theory. In particular, the radiated gravity waves are found to produce a leading-order back action on the source, and this feedback effect, completely ignored in the acoustic analogy type of approach, is naturally taken into account by the triple-deck formalism. A by-product is that for certain incident angles, gravity waves are over-reflected by the boundary layer, i.e. the reflected waves are stronger than the incident waves.

scholarly journals Energy Exchanges between Density Fronts and Near-Inertial Waves Reflecting off the Ocean Surface

2016 ◽  
Vol 46 (2) ◽  
pp. 501-516 ◽  
Author(s):  
Nicolas Grisouard ◽  
Leif N. Thomas
Keyword(s):  
Analytical Model ◽  
Internal Waves ◽  
Energy Exchange ◽  
Viscous Friction ◽  
Nonlinear Effects ◽  
Ocean Surface ◽  
Inertial Waves ◽  
Viscous Effects ◽  
Reflected Waves ◽  
Incident Waves

AbstractInertial waves propagating upward in a geostrophically balanced front experience critical reflections against the ocean surface. Such reflections naturally create oscillations with small vertical scales, and viscous friction becomes a dominant process. Here, friction modifies the polarization relations of internal waves and allows energy from the balanced front to be exchanged with the ageostrophic motions and eventually dissipated. In addition, while in the well-known inviscid case internal waves propagate on only two characteristics, this study demonstrates using an analytical model that strong viscous effects introduce additional oscillatory modes that can exchange energy with the front. Moreover, during a linear, near-critical reflection, the superposition of several of these oscillations induces an even stronger energy exchange with the front. When the Richardson number based on the frontal thermal wind shear is O(1), the rate of energy exchange peaks at wave frequencies that are near inertial and is comparable in magnitude to the energy flux of the incident, upward-propagating waves. Two-dimensional, linear numerical experiments confirm this finding. The analytical model also demonstrates that this process is qualitatively insensitive to the actual value of the viscosity or the form of the boundary condition at the surface. In fully nonlinear experiments, the authors recover these qualitative conclusions. However, nonlinear wave–wave interactions and turbulence in particular, strongly modify the amount of energy that is exchanged with the front. In practice, such nonlinear effects are only active when the incident waves have frequencies higher than the Coriolis frequency, since these configurations are conducive to near-resonant triad interactions between incident and reflected waves.

scholarly journals Note on total reflexion of electric waves at the interface between two media

1928 ◽  
Vol 119 (783) ◽  
pp. 523-525
Keyword(s):  
Wave Front ◽  
Electric Force ◽  
Present Communication ◽  
Reflected Waves ◽  
Magnetic Forces ◽  
Previous Communication ◽  
Total Reflexion ◽  
Incident Waves ◽  
Electric Waves

In a previous communication it was assumed that, when total reflexion takes place at the interface between two media, the electric force in the disturbance in the second medium is in the plane of the wave-front; it may be shown that it is impossible in this case to satisfy the conditions that the electric and magnetic forces are both in the wave-front in the second medium. The object of the present communication is to investigate the disturbance in the second medium, and to obtain the changes of phase in the reflected waves in the first medium. Taking the plane z = 0 as the interface between the two media, let the components of the electric force in the incident waves, z > 0, be given by (A, B, C) cos K ( lx + my + nz + V t )

scholarly journals VISCOUS MODIFIED COSMIC CHAPLYGIN GAS COSMOLOGY

2013 ◽  
Vol 22 (09) ◽  
pp. 1350061 ◽  
Author(s):  
B. POURHASSAN
Keyword(s):  
Dark Energy ◽  
Energy Density ◽  
Nonlinear Equation ◽  
Observational Data ◽  
Function Method ◽  
Chaplygin Gas ◽  
Time Dependent ◽  
Dark Energy Density ◽  
Hubble Expansion ◽  
Exponential Function Method

In this paper, we construct viscous modified cosmic Chaplygin gas as a model of dark energy. We use exponential function method to solve nonlinear equation and obtain time-dependent dark energy density. Then, we discuss Hubble expansion parameter and scale factor and fix them by using observational data. Effect of viscosity to the evolution of Universe is investigated. We also investigate stability of this theory.

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