Small perturbation wave propagation in variable modulus statically stressed media. Plane waves

1989 ◽  
Vol 25 (3) ◽  
pp. 222-230
Author(s):  
A. I. Oleinikov
Keyword(s):  
Wave Propagation ◽  
Small Perturbation ◽  
Plane Waves ◽  
Perturbation Wave ◽  
Variable Modulus

Constitutive Models for Wave Propagation in Soils

2006 ◽  
Vol 59 (3) ◽  
pp. 146-175 ◽  
Author(s):  
Frederick Bloom
Keyword(s):  
Wave Propagation ◽  
Entire Range ◽  
Constitutive Models ◽  
Volume Distribution ◽  
Single Model ◽  
Function Model ◽  
Material Models ◽  
Elastic Plastic ◽  
Variable Modulus ◽  
Loading And Unloading

A survey is provided of the various constitutive models that have been used to study the phenomena of wave propagation in soils. While different material models have been proposed for the response of soils, it is now generally understood that no single model may be used over the entire range of pressures which are typically studied. The constitutive models reviewed in this paper include a number of effective stress and multiphase models, the volume distribution function model, and various versions of the P−α model. Also discussed are classical elastic-plastic models, models possessing different elastic constants in loading and unloading, variable modulus models, and capped elastic-plastic models.

Plane Waves in an Elastic-Plastic Half-Space Due to Combined Surface Pressure and Shear

1966 ◽  
Vol 33 (1) ◽  
pp. 149-158 ◽  
Author(s):  
H. H. Bleich ◽  
Ivan Nelson
Keyword(s):  
Wave Propagation ◽  
Differential Equations ◽  
Half Space ◽  
Nonlinear Differential Equations ◽  
Plane Waves ◽  
Yield Condition ◽  
Shear Stresses ◽  
Von Mises ◽  
Plane Wave Propagation ◽  
Normal And Shear Stresses

The most general case of plane wave propagation, when normal and shear stresses occur simultaneously, is considered in a material obeying the von Mises yield condition. The resulting nonlinear differential equations have not been solved previously for any boundary-value problem, except for special situations where the differential equations degenerate into linear ones. In the present paper, the stresses in a half-space, due to a uniformly distributed step load of pressure and shear on the surface, are obtained in closed form.

Magneto-thermo-elastic plane waves

1965 ◽  
Vol 61 (4) ◽  
pp. 939-944 ◽  
Author(s):  
C. M. Purushothama
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Shear Wave ◽  
Wave Velocity ◽  
Compression Wave ◽  
Thermal Field ◽  
Plane Waves ◽  
Elastic Plane ◽  
Magnetic Diffusivity ◽  
The Magnetic Field

AbstractThe combined effects of uniform thermal and magnetic fields on the propagation of plane waves in a homogeneous, initially unstressed, electrically conducting elastic medium have been investigated.When the magnetic field is parallel to the direction of wave propagation, the compression wave is purely thermo-elastic and the shear wave is purely magneto-elastic in nature. For a transverse magnetic field, the shear waves remain elastic whereas the compression wave assumes magneto-thermo-elastic character due to the coupling of all the three fields—mechanical, magnetic and thermal. In the general case, the waves polarized in the plane of the direction of wave propagation and the magnetic field are not only coupled but are also influenced by the thermal field, once again exhibiting the coupling of the three fields. The shear wave polarized transverse to the plane retains its magneto-elastic character.Notation.Hi = primary magnetic field components,ht = induced magnetic field components,To = initial thermal field,θ = induced thermal field,C = compression wave velocity.S = shear wave velocity,ui = displacement components,cv = specific heat at constant volume,k = thermal conductivity,η = magnetic diffusivity,μe = magnetic permeability,λ, μ = Lamé's constants,β = ratio of coefficient of volume expansion to isothermal compressibility.

Nonlinear Wave Propagation in Elastic Submerged Cables

1997 ◽  
Author(s):  
M. Behbahani-Nejad ◽  
N. C. Perkins
Keyword(s):  
Wave Propagation ◽  
Linear Theory ◽  
Fluid Model ◽  
Plane Waves ◽  
Three Dimensional ◽  
Hydrodynamic Drag ◽  
Far Field ◽  
Computational Domain ◽  
Nonlinear Wave Propagation ◽  
Closed Form Solutions

Abstract This paper analyzes the coupled nonlinear tangential-normal waves that propagate along underwater cable suspensions. Taken with the recently developed linear theory governing the in-plane structural waves (3) and an analysis of nonlinear out-of-plane waves for submerged cables (2), this investigation contributes further understanding toward a nonlinear three-dimensional theory for wave propagation along fluid loaded cables. The nonlinearities present in the in-plane model render the cable/fluid model intractable by exact analytical methods. A numerical solution is pursued in this study using finite difference algorithms. To this end, an infinite cable domain is divided to two sub domains, namely an interior (finite computational) domain and exterior (infinite far field) domain. Closed-form solutions for the approximate linear theory are employed for the far field in constructing nonreflecting boundary conditions for the computational domain. Numerical results highlight the governing role of nonlinear hydrodynamic drag for underwater cable suspentions.

Elastic-wave propagation in deviated wells in anisotropic formations

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. D191-D202 ◽  
Author(s):  
Bikash K. Sinha ◽  
Ergün Şimşek ◽  
Qing-Huo Liu
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Plane Waves ◽  
Elastic Wave Propagation ◽  
Dipole Source ◽  
Heavy Fluid ◽  
Flexural Mode ◽  
Low Frequencies ◽  
Wave Velocities ◽  
Anisotropic Formation

A finite-difference time-domain (FDTD) formulation with perfectly matched layer (PML) enables analysis of elastic-wave propagation in a fluid-filled borehole in an arbitrarily anisotropic formation. The FDTD formulation yields synthetic waveforms at an array of receivers produced by a monopole or dipole source placed on the borehole axis. Synthetic waveforms are then processed by a modified matrix pencil algorithm to isolate both nondispersive and dispersive arrivals in the wavetrain. The processing algorithm used in this study extracts phase slownesses of plane waves that agree well with the corresponding phase slownesses calculated for propagation along an arbitrary direction in an anisotropic formation. The tube-wave phase velocity obtained from the zero-frequency intercept of the Stoneley dispersion compares well with the analytical results for deviated wellbores in both fast and slow transversely isotropic (TI) formations. Good agreement is also obtained between the low-frequencyasymptotes of borehole flexural dispersion and the corresponding shear-wave velocities from a numerically exact solution of Kelvin-Christoffel equations for plane-wave velocities in anisotropic formations. Numerical results indicate that the Stoneley dispersion changes by a rather small amount, whereas the dipole flexural dispersions exhibit larger changes with wellbore deviations. The influence of a sonic tool structure on borehole elastic-waves can be described by an equivalent heavy-fluid column placed concentrically with the borehole axis. The effect of a heavy-fluid column on the borehole flexural mode is larger in fast than in slow formations. However, the Stoneley dispersion at low frequencies is affected by the presence of the tool structure in both the fast and slow formations. The present study confirms that the two orthogonal dipole flexural dispersions are nearly parallel to each other in slow formations and nonintersecting in fast formations, even in deviated wellbores and in the presence of a sonic tool structure described by a heavy-fluid column.

The Method of Generalized Ray-Revisited

2000 ◽  
Vol 16 (1) ◽  
pp. 37-44
Author(s):  
Franz Ziegler ◽  
Piotr Borejko
Keyword(s):  
Wave Propagation ◽  
Parallel Computing ◽  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Plane Waves ◽  
Solution Technique ◽  
New Developments ◽  
Infinite Space ◽  
Layered Half Space

ABSTRACTBased on a landmark paper by Pao and Gajewski, some novel developments of the method of generalized ray integrals are discussed. The expansion of the dynamic Green's function of the infinite space into plane waves allows benchmark 3-D solutions in the layered half-space and even enters the background formulation of elastic-viscoplastic wave propagation. New developments of software of combined symbolic-numerical manipulation and parallel computing make the method a competitive solution technique.

The propagation of magneto-thermo-viscoelastic plane waves in a parallel union of the Kelvin and Maxwell bodies

1971 ◽  
Vol 70 (2) ◽  
pp. 343-350 ◽  
Author(s):  
D. S. Chandrasekhariah
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Electromagnetic Field ◽  
Wave Propagation ◽  
Thermal Field ◽  
Plane Waves ◽  
Viscoelastic Body ◽  
Longitudinal Component ◽  
Transverse Component ◽  
Wave Travel

AbstractThe propagation of plane waves in a viscoelastic body representing a parallel union of the Kelvin and Maxwell bodies placed in a magneto-thermal field is investigated. It is shown that the longitudinal component of the wave is in general coupled with a transverse component and the wave travels in two families. In particular if the primary magnetic field is either parallel or perpendicular to the direction of wave propagation, the three components of the wave travel unlinked, with either the longitudinal component or the transverse components unaffected by the presence of the electromagnetic field. If the electrical conductivity of the solid is infinite the effect of the primary magnetic field is to increase the values of the material constants. The effect of wave propagation on magnetic permeability is equivalent to an anisotropic rescaling of the primary magnetic field. Some of the results obtained in the earlier works are obtained as particular cases of the more general results derived here.

scholarly journals Temporal Frequency Spread of Plane Wave Propagation through Moderate to Strong Turbulence

2019 ◽  
Vol 8 (2S8) ◽  
pp. 1944-1947
Keyword(s):  
Wave Propagation ◽  
Temporal Frequency ◽  
Plane Waves ◽  
Energy Regulation ◽  
Anisotropic Component ◽  
Frequency Spread ◽  
Strong Turbulence ◽  
Kolmogorov Turbulence ◽  
Simulation Results ◽  
Plane Wave Propagation

In this study, we derive new expressions for the atmospheric-brought on frequency unfold of plane waves propagating thru slight to strong turbulence in a horizontal direction based on the modified anisotropic non-Kolmogorov electricity spectrum as antagonistic to conventional Kolmogorov electricity spectrum. The energy regulation price varies from three to 4 instead of the traditional Kolmogorov power law price; the general amplitude price differs from the conventional Kolmogorov regular cost 0.033. these new expressions are based on slight to robust fluctuation vicinity and anisotropic non-Kolmogorov turbulence. The simulation results show that temporal frequency unfold will decrease even as the anisotropic component   2  is increasing

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