Low-frequency scattering on a half-space filled with periodical inclined elastic layers with the slip on boundaries

Author(s):  
Yu. Roganov ◽  
V. Roganov
1971 ◽  
Vol 38 (3) ◽  
pp. 608-614 ◽  
Author(s):  
Y. C. Pao ◽  
Ting-Shu Wu ◽  
Y. P. Chiu

This paper is concerned with the plane-strain problem of an elastic layer supported on a half-space foundation and indented by a cylinder. A study is presented of the effect of the contact condition at the layer-foundation interface on the contact stresses of the indented layer. For the general problem of elastic indenter or elastic foundation, the integral equations governing the contact stress distribution of the indented layer derived on the basis of two-dimensional theory of elasticity are given and a numerical method of solution is formulated. The limiting contact conditions at the layer-foundation interface are then investigated by considering two extreme cases, one with the indented layer in frictionless contact with the half space and the other with the indented layer rigidly adhered to the half space. Graphs of the bounds on the maximum normal stress occurring in indented elastic layers for the cases of rigid cylindrical indenter and rigid half-space foundation are obtained for possible practical applications. Some results of the elastic indenter problem are also presented and discussed.


2020 ◽  
Vol 62 (1) ◽  
pp. 272-275
Author(s):  
Blagoja Markovski ◽  
Leonid Grcev ◽  
Vesna Arnautovski-Toseva

1999 ◽  
Vol 09 (05) ◽  
pp. 755-798 ◽  
Author(s):  
A. S. BONNET-BEN DHIA ◽  
J. DUTERTE ◽  
P. JOLY

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.


1962 ◽  
Vol 29 (1) ◽  
pp. 53-60 ◽  
Author(s):  
Julius Miklowitz

The problem treated is that of an infinite free plate excited symmetrically by two equal and normally opposed step point-loads on its faces. The problem is equivalent to that of the surface normal point-load excitation of an infinite elastic layer, half the thickness of the plate, overlying a rigid half-space with lubricated contact. The formal solution is obtained from the equations of motion in linear elasticity with the aid of a double integral transform technique and residue theory. The stationary phase method, and known characteristics of the governing Rayleigh-Lamb frequency equation, are used to analyze and evaluate numerically the far field displacements. It is shown that the head of the disturbance is composed predominantly of the low-frequency long waves from the lowest mode of wave transmission.


1971 ◽  
Vol 38 (1) ◽  
pp. 111-117 ◽  
Author(s):  
A. O. Awojobi

The mixed boundary-value problems of the vibrations of rigid bodies on elastic media are generally considered in the low-frequency-factor range. It is first established that, quite apart from a consideration of resonance, the usual assumption that this range predominates in practice is erroneous. The present work, therefore, is concerned with vibrations at frequency factors which are much greater than unity. Five cases have been considered: torsional vibration of a rigid circular body on a semi-infinite elastic medium and on an infinitely wide elastic stratum on a rigid bed; vertical vibration of a rigid circular body and of an infinitely long rectangular body on a semi-infinite elastic medium; rocking of a long rectangular body on a semi-infinite elastic medium. An estimate of both the unknown dynamic stress distribution under the rigid bodies and their amplitude responses has been obtained by finding an approximate solution to the exact governing dual integral equations. It is shown that at high-frequency factors, stress distributions are approximately constant for vertical vibrations and vary linearly from the center for rotational vibrations as in a Winkler model of theoretical soil statics contrary to increasing stresses with infinite edge stresses for low-frequency and static stress distributions of rigid bodies on elastic half space. We also obtain the important conclusion for amplitude response that it is predominantly governed by the inertia of the bodies because the contribution due to the dispersion of waves in the elastic medium is generally of a lower order of frequency factor than the inertia term except for an incompressible medium which has been analyzed separately and found to be of the same order leading to expressions for equivalent inertia of the vibrating medium. The theoretical results are used to derive the “tails” of resonance curves for both half space and stratum cases where experimental results are available. The agreement is fair and improves with increasing frequency factor.


Geophysics ◽  
2007 ◽  
Vol 72 (3) ◽  
pp. F119-F126 ◽  
Author(s):  
Yusen Ley-Cooper ◽  
James Macnae

We aim to develop a quantitative method for recalibration of historic helicopter electromagnetic data sets. Recent research has shown that frequency-domain helicopter electromagnetic data collected over a conductive half-space such as calm seawater can be used to correct system calibration errors. However, most historic surveys consist only of data collected over land, where the conductive half-space assumption is rarely justified. We estimate the required recalibration parameters by analyzing systematic misfits in the inversion of statistically chosen measures of historic data. Our method requires the identification, within the survey area, of a zone of conductive responses that are reasonably uniform. From this zone, a set of altitude-corrected median responses are estimated. These are inverted using geologically specifiedconstraints to obtain a best-fit layered earth model. Systematic inconsistencies between the median measured altitude and the inverted depth to surface are attributed to altitude error. Remaining frequency-dependent fitting errors are assumed to be the calibration errors. We tested the method with partial success on helicopter electromagnetic data sets collected over uniform deep sediments where seawater data were also available and two different inland surveys over multiple lithologies in one general area. At high frequencies, our method works reliably. Recalibration of low-frequency data is not possible if the area used as a reference consists of moderate or poor conductors. In this case, data amplitudes are small and are greatly affected by imperfect drift and magnetic susceptibility corrections. Historic helicopter electromagnetic data may require amplitude rescaling up to 20%–30%, with phase shifts of up to 3°.


Sign in / Sign up

Export Citation Format

Share Document