A note on the approximate determination of the dispersion of Love waves in a laterally nonhomogeneous layer lying over a homogeneous half-space

1980 ◽  
Vol 118 (2) ◽  
pp. 1170-1178
Author(s):  
T. K. De
Keyword(s):  
Half Space ◽  
Love Waves ◽  
Approximate Determination ◽  
Homogeneous Half Space ◽  
Nonhomogeneous Layer

APPROXIMATE DETERMINATION OF GEOMETRIC PARAMETERS OF THE SAG FOLLOWING THE EMBEDDING OF A PARABOLOID INDENTER INTO A HALF-SPACE

2021 ◽  
pp. 39-47
Author(s):  
Ali Yu. Albagachiev ◽  
◽  
A.M. Moiseenko ◽  
E.V. Zernov ◽  
A.V. Lut’yanov ◽  
...  
Keyword(s):  
Surface Layer ◽  
Analytical Solution ◽  
Half Space ◽  
Strain State ◽  
Geometric Parameters ◽  
Approximate Determination ◽  
Depth Of Penetration ◽  
Stress Strain ◽  
Stress Strain State

The problem of the indenter embedding into a half-space is formulated and solved. A concept of the elastic contact is used, which implies the uniformity of the stress-strain state in a surface layer. The process of the surface layer formation after mechanical treatment is studied. Based on the general theory of indenter penetration into a half-space, numerical and analytical solutions, determining the length and depth of penetration of a paraboloid into elastoplastic space, are obtained. According to the theory of indentation, the problem is reduced to the use of the method of approximate determination of geometric parameters of a bead, when a paraboloid is being embedded into elastoplastic space. An exact solution to the formulated problem allows one to obtain analytical dependences for calculating the velocities and to study the stress-strain state of the material in the half-space surface layer during the processing. The reliability of the obtained analytical solution is confirmed by numerical calculations without introducing additional hypotheses. Based on the analytical solution, the geometric parameters of the influx from the penetration depth are determined. Calculations can be performed at any embedding depth. Sag formation during the indenter embedding by 18 mm into plasticine specimens is considered as an example. It is shown that the rigid zone is insignificant or absent.

Dispersion of Love waves in prestressed double-layered medium over a gravitating half-space

2020 ◽  
Vol 13 (13) ◽  
Author(s):  
Bishwanath Prasad ◽  
Santimoy Kundu ◽  
Prakash Chandra Pal ◽  
Parvez Alam
Keyword(s):  
Half Space ◽  
Layered Medium ◽  
Love Waves

scholarly journals Group and Phase Velocity of Love Waves Propagating in Elastic Functionally Graded Materials

2015 ◽  
Vol 40 (2) ◽  
pp. 273-281 ◽  
Author(s):  
Piotr Kiełczyński ◽  
Marek Szalewski ◽  
Andrzej Balcerzak ◽  
Krzysztof Wieja
Keyword(s):  
Group Velocity ◽  
Half Space ◽  
Functionally Graded Materials ◽  
Integral Formula ◽  
Liouville Problem ◽  
Elastic Half Space ◽  
Functionally Graded ◽  
Love Waves ◽  
Graded Materials ◽  
Sturm Liouville

AbstractThis paper presents a theoretical study of the propagation behaviour of surface Love waves in nonhomogeneous functionally graded elastic materials, which is a vital problem in acoustics. The elastic properties (shear modulus) of a semi-infinite elastic half-space vary monotonically with the depth (distance from the surface of the material). Two Love wave waveguide structures are analyzed: 1) a nonhomogeneous elastic surface layer deposited on a homogeneous elastic substrate, and 2) a semi-infinite nonhomogeneous elastic half-space. The Direct Sturm-Liouville Problem that describes the propagation of Love waves in nonhomogeneous elastic functionally graded materials is formulated and solved 1) analytically in the case of the step profile, exponential profile and 1cosh2type profile, and 2) numerically in the case of the power type profiles (i.e. linear and quadratic), by using two numerical methods: i.e. a) Finite Difference Method, and b) Haskell-Thompson Transfer Matrix Method.The dispersion curves of phase and group velocity of surface Love waves in inhomogeneous elastic graded materials are evaluated. The integral formula for the group velocity of Love waves in nonhomogeneous elastic graded materials has been established. The results obtained in this paper can give a deeper insight into the nature of Love waves propagation in elastic nonhomogeneous functionally graded materials.

The Approximate Determination of the Resistance of an Irregular Conductor

1914 ◽  
Vol 4 (4) ◽  
pp. 391-395
Author(s):  
J. F. H. Douglas
Keyword(s):  
Approximate Determination

The harmonic and transient electromagnetic response of a thin dipping dike

Geophysics ◽  
1983 ◽  
Vol 48 (7) ◽  
pp. 934-952 ◽  
Author(s):  
P. Weidelt
Keyword(s):  
Formal Solution ◽  
Harmonic Excitation ◽  
Electromagnetic Response ◽  
Approximate Determination ◽  
Finite Conductivity ◽  
Circular Loop ◽  
Decay Modes ◽  
Transient Electromagnetic ◽  
Free Decay

An exact solution is given for the electromagnetic induction in a dipping dike of finite conductivity, represented as a thin half‐sheet in a nonconducting surrounding. The problem is formulated for arbitrary dipole or circular loop [Formula: see text] configurations. The formal solution obtained by the Wiener‐Hopf technique is cast into a rapidly convergent triple integral suitable for an effective numerical treatment. A good agreement is found between numerical results and analog measurements available for harmonic excitation. The transient response is obtained as a superposition of the half‐sheet free‐decay modes and is illustrated by some numerical examples for coincident loops, including a diagram for the approximate determination of conductance and depth of a vertical dike.

Inversion of slingram electromagnetic induction data using a Born approximation

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. E201-E212 ◽  
Author(s):  
Jochen Kamm ◽  
Michael Becken ◽  
Laust B. Pedersen
Keyword(s):  
Half Space ◽  
Born Approximation ◽  
High Efficiency ◽  
Three Dimensions ◽  
Background Model ◽  
Desktop Computer ◽  
Near Surface ◽  
Homogeneous Half Space ◽  
Integral Equation Formulation ◽  
Forward Operator

We present an efficient approximate inversion scheme for near-surface loop-loop EM induction data (slingram) that can be applied to obtain 2D or 3D models on a normal desktop computer. Our approach is derived from a volume integral equation formulation with an arbitrarily conductive homogeneous half-space as a background model. The measurements are not required to fulfill the low induction number condition (low frequency and conductivity). The high efficiency of the method is achieved by invoking the Born approximation around a half-space background. The Born approximation renders the forward operator linear. The choice of a homogeneous half-space yields closed form expressions for the required electromagnetic normal fields. It also yields a translationally invariant forward operator, i.e., a highly redundant Jacobian. In connection with the application of a matrix-free conjugate gradient method, this allows for very low memory requirements during the inversion, even in three dimensions. As a consequence of the Born approximation, strong conductive deviations from the background model are underestimated. Highly resistive anomalies are in principle overestimated, but at the same time difficult to resolve with induction methods. In the case of extreme contrasts, our forward model may fail in simultaneously explaining all the data collected. We applied the method to EM34 data from a profile that has been extensively studied with other electromagnetic methods and compare the results. Then, we invert three conductivity maps from the same area in a 3D inversion.

Caracterización de la roca mediante propiedades físicas y su relación con la resistencia a la compresión simple

2021 ◽  
Vol 2 (4) ◽  
pp. 5081-5093
Author(s):  
Patricio Feijoo Calle ◽  
Elizabeth Brito Verdezoto
Keyword(s):  
Compressive Strength ◽  
Physical Properties ◽  
Unconfined Compressive Strength ◽  
Approximate Determination ◽  
Practical Application ◽  
Calculation Methodology

En este trabajo se propone una metodología sencilla y de aplicación práctica en campo para la determinación aproximada de la Resistencia a la Compresión Simple (RCS) en rocas, propiedad o característica que es importante en minería, ya que mediante la misma, se ejecutan análisis para la valoración de factores de seguridad y estabilidad y/o posibles sistemas de fortificación en las obras o estructuras mineras, a más de que la caracterización de la RCS es también influyente en el uso de explosivos para la explotación o extracción de materiales de una cantera o mina. Esta estimación se la propone en base a la determinación de las siguientes tres propiedades de la roca, que en esta investigación las denominamos densidad, porosidad y absorción “en mina”. Estas propiedades físicas se las puede obtener de una forma simple, pero metódica y en este trabajo se han ejecutado ensayos sobre un mismo material o roca proveniente de la zona de Cojitambo, provincia del Cañar (Ecuador) y sobre una base de 60 muestras o probetas. Los resultados obtenidos permiten una correlación entre las propiedades antes descritas y la RCS, a más que se ha estructurado una metodología de cálculo para el objetivo planteado.   This work proposes a simple methodology and practical application in the field for the approximate determination of the Unconfined Compressive Strength (UCS) in rocks, property or characteristic that is important in mining, since through it analyzes are carried out to the assessment of security and stability factors and/or possible fortification systems in the works or mining structures, in addition to the characterization of the UCS is also influential in the use of explosives for the exploitation or extraction of materials from a quarry or mine. This estimate is proposed based on the determination of the following three properties of the rock, which in this investigation we call density, porosity and absorption “in mine”. These physical properties can be obtained in a simple, but methodical way and in this work, tests have been carried out on the same material or rock from the Cojitambo area, Cañar province (Ecuador) and on the basis of 60 samples or test tubes. The results obtained allow a correlation between the properties described above and the UCS, in addition to a calculation methodology for the proposed objective.

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