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.

The displacement field due to a point load at the interface of a two layer elastic half-space

Géotechnique ◽  
1978 ◽  
Vol 28 (1) ◽  
pp. 43-56 ◽  
Author(s):  
T. G. Davies ◽  
P. K. Banerjee
Keyword(s):  
Half Space ◽  
Displacement Field ◽  
Elastic Half Space ◽  
Point Load

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.

How fault creep makes its way!

2020 ◽  
Author(s):  
Sohom Ray ◽  
Dmitry Garagash
Keyword(s):  
Free Surface ◽  
Steady State ◽  
High Stress ◽  
Slip Rate ◽  
Interfacial Strength ◽  
Elastic Half Space ◽  
Entire Length ◽  
Fault Creep ◽  
Dynamic Event ◽  
First Case

<p>We model mechanics of an aseismic fault creep propagation and conditions when it may lead to the initiation of seismic slip. We do so by considering fault bounding medium to be elastically deformable and fault's interfacial strength to be slip rate- and state-dependent characterized by the steady-state rate-weakening. The fault is considered to be initially locked: a state of slip when interfacial slip velocity is considerably low and arbitrarily less than the steady-state sliding rate for given uniformly distributed prestress.</p><p>We find solutions for creep penetration into the fault under geologically relevant loading scenarios (e.g., that of a plate-bounding strike-slip faulting driven by the slip at depth, or that of a rate-weakening patch of a fault loaded by a creep on an adjacent rate-strengthening part due to, e.g., anthropogenic fluid injection). In all the cases, the creep makes its way as a self-similar traveling front characterized by high stress owed to the direct effect; however, the remaining creep profile exhibits a near steady-state sliding. This may imply that a choice from a set of rules for the evolution of state variable—with identical linearizations about steady-state sliding—has no bearing on the creep penetration. Further, we find that the prestress, close to or far from steady-state sliding stress, controls the rate and manner of the creep penetration.</p><p>We study slip propagation from an imposed dislocation accrued at a constant rate at one end of a homogeneous fault with the other end either at (1) the free surface of an elastic half-space or (2) strictly locked (buried) in the elastic full space. In both scenarios, no slip instability takes place over aseismic creep propagation distances relatable to the usual elasto-frictional nucleation lengthscale (e.g. Rubin & Ampuero 2005). Instead, in the first case creep propagation leads to the nucleation of the first and all subsequent dynamic events of the emerging cycle at/near the free surface after the creep traversed the entire length of the fault. In the second case, the creep front traverses nearly the entire length of the fault, but, instead of nucleating a dynamic event, the front arrests at some distance from the buried fault end, followed by the continual accumulation of aseismic slip without ever nucleating a dynamic event. These results may be owed to the physical and geometrical invariance of the considered homogeneous fault and may signal the essential role of fault strength heterogeneity, either that of the normal stress and/or frictional properties (Ray & Viesca, 2017, 2019), in defining its seismogenic character, i.e. under which conditions and where on the fault the earthquake slip instability can take place. </p>

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