scholarly journals Erratum to “Propagation of P waves from stress-free surface elastic half-space with voids under thermal relaxation and magnetic field [Appl. Math. Model. 34 (2010) 1798–1806]

2011 ◽  
Vol 35 (12) ◽  
pp. 5920
Author(s):  
S.M. Abo-Dahab
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Half Space ◽  
Thermal Relaxation ◽  
Elastic Half Space ◽  
P Waves ◽  
Math Model ◽  
Appl Math

scholarly journals Effects of a magnetic field and initial stress on reflection of SV-waves at a free surface with voids under gravity

2018 ◽  
Vol 27 (5-6) ◽  
Author(s):  
Augustine Igwebuike Anya ◽  
M.W. Akhtar ◽  
Syed Muhammad Abo-Dahab ◽  
Hajra Kaneez ◽  
Aftab Khan ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Magnetic Fields ◽  
Initial Stress ◽  
Half Space ◽  
Significant Role ◽  
Elastic Half Space ◽  
Wave Incident ◽  
P Waves

AbstractThe present study deals with the reflection of SV-waves at a free surface in the presence of magnetic field, initial stress, voids and gravity. When an SV-wave incident on the free surface of an elastic half space, two damped P-waves and an SV-wave are reflected. Among these waves, P-waves are only affected by magnetic fields whereas SV-waves are influenced by both, initial stress and magnetic fields. Effect of gravity is negligible whereas voids played a significant role. These observations can be helpful for seismology and earthquake sciences.

Magneto-elastic SV-wave at the interface of pre-stressed surface with voids under rotation

2016 ◽  
Vol 25 (5-6) ◽  
pp. 153-160
Author(s):  
Rajneesh Kakar ◽  
Shikha Kakar
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Initial Stress ◽  
Seismic Waves ◽  
Elastic Half Space ◽  
Amplitude Ratios ◽  
P Waves ◽  
Stress Rotation ◽  
Acoustic Device ◽  
Stressed Surface

AbstractThe aim of this paper is to study the behaviour of reflection of SV- wave at a free surface under the effects of magnetic field, initial stress, rotation and voids. When a SV- wave is incident on the free surface of an elastic half space, two damped P-waves and a SV-wave is reflected. Among of these waves, P-waves are only affected by magnetic field and rotation whereas SV-wave is influenced by rotation, initial stress and magnetic field. Numerical computations are performed for the developed amplitude ratios of P-, SV- and magneto-elastic waves. This study would be useful for magneto-elastic acoustic device field and further study about nature of seismic waves.

scholarly journals Transient Excitation of an Elastic Half Space by a Point Load Traveling on the Surface

1969 ◽  
Vol 36 (3) ◽  
pp. 505-515 ◽  
Author(s):  
D. C. Gakenheimer ◽  
J. Miklowitz
Keyword(s):  
Exact Solution ◽  
Free Surface ◽  
Steady State ◽  
Wave Front ◽  
Half Space ◽  
Displacement Field ◽  
Elastic Half Space ◽  
Point Load ◽  
Limit Case ◽  
Transient Waves

The propagation of transient waves in a homogeneous, isotropic, linearly elastic half space excited by a traveling normal point load is investigated. The load is suddenly applied and then it moves rectilinearly at a constant speed along the free surface. The displacements are derived for the interior of the half space and for all load speeds. Wave-front expansions are obtained from the exact solution, in addition to results pertaining to the steady-state displacement field. The limit case of zero load speed is considered, yielding new results for Lamb’s point load problem.

scholarly journals Dynamic Stress and Displacement in an Elastic Half-Space with a Cylindrical Cavity

2011 ◽  
Vol 18 (6) ◽  
pp. 827-838 ◽  
Author(s):  
İ. Coşkun ◽  
H. Engin ◽  
A. Özmutlu
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Half Space ◽  
Cylindrical Cavity ◽  
Circular Cross Section ◽  
Elastic Half Space ◽  
Least Square ◽  
Polar Coordinates ◽  
Wave Number ◽  
Forcing Function

The dynamic response of an elastic half-space with a cylindrical cavity in a circular cross-section is analyzed. The cavity is assumed to be infinitely long, lying parallel to the plane-free surface of the medium at a finite depth and subjected to a uniformly distributed harmonic pressure at the inner surface. The problem considered is one of plain strain, in which it is assumed that the geometry and material properties of the medium and the forcing function are constant along the axis of the cavity. The equations of motion are reduced to two wave equations in polar coordinates with the use of Helmholtz potentials. The method of wave function expansion is used to construct the displacement fields in terms of the potentials. The boundary conditions at the surface of the cavity are satisfied exactly, and they are satisfied approximately at the free surface of the half-space. Thus, the unknown coefficients in the expansions are obtained from the treatment of boundary conditions using a collocation least-square scheme. Numerical results, which are presented in the figures, show that the wave number (i.e., the frequency) and depth of the cavity significantly affect the displacement and stress.

MATHEMATICAL ANALYSIS OF ELASTIC SURFACE WAVES IN TOPOGRAPHIC WAVEGUIDES

1999 ◽  
Vol 09 (05) ◽  
pp. 755-798 ◽  
Author(s):  
A. S. BONNET-BEN DHIA ◽  
J. DUTERTE ◽  
P. JOLY
Keyword(s):  
Free Surface ◽  
Half Space ◽  
Guided Waves ◽  
Transverse Energy ◽  
Eigenvalue Problems ◽  
Low Frequency ◽  
Elastic Half Space ◽  
High Frequencies ◽  
Guided Mode ◽  
Adjoint Operators

We present here a theoretical study of the guided waves in an isotropic homogeneous elastic half-space whose free surface has been deformed. The deformation is supposed to be invariant in the propagation direction and localized in the transverse ones. We show that finding guided waves amounts to solving a family of 2-D eigenvalue problems set in the cross-section of the propagation medium. Then using the min-max principle for non-compact self-adjoint operators, we prove the existence of guided waves for some particular geometries of the free surface. These waves have a smaller speed than that of the Rayleigh wave in the perfect half-space and a finite transverse energy. Moreover, we prove that the existence results are valid for arbitrary high frequencies in the presence of singularities of the free boundary. Finally, we prove that no guided mode can exist at low frequency, except maybe the fundamental one.

scholarly journals Magneto-thermoelastic waves in a perfectly conducting elastic half-space in thermoelasticity III

2005 ◽  
Vol 2005 (20) ◽  
pp. 3303-3318
Author(s):  
S. K. Roychoudhuri ◽  
Nupur Bandyopadhyay
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Wave Front ◽  
Half Space ◽  
Temperature Stress ◽  
Elastic Half Space ◽  
Small Time ◽  
Dilatational Wave ◽  
Heat Transport Equation ◽  
Perturbed Magnetic Field

The propagation of magneto-thermoelastic disturbances in an elastic half-space caused by the application of a thermal shock on the stress-free bounding surface in contact with vacuum is investigated. The theory of thermoelasticity III proposed by Green and Naghdi is used to study the interaction between elastic, thermal, and magnetic fields. Small-time approximations of solutions for displacement, temperature, stress, perturbed magnetic fields both in the vacuum and in the half-space are derived. The solutions for displacement, temperature, stress, perturbed magnetic field in the solid consist of a dilatational wave front with attenuation depending on magneto-thermoelastic coupling and also consists of a part diffusive in nature due to the damping term present in the heat transport equation, while the perturbed field in vacuum represents a wave front without attenuation traveling with Alfv'en acoustic wave speed. Displacement and temperatures are continuous at the elastic wave front, while both the stress and the perturbed magnetic field in the half-space suffer finite jumps at this location. Numerical results for a copper-like material are presented.

A normal crack in an elastic half-space with stress-free surface

1993 ◽  
Vol 16 (8) ◽  
pp. 563-579 ◽  
Author(s):  
P. A. Martin ◽  
L. Päivärinta ◽  
S. Rempel
Keyword(s):  
Free Surface ◽  
Half Space ◽  
Elastic Half Space
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