Lamb’s problem: a brief history

Emami, Mohamad; Eskandari‐Ghadi, Morteza

doi:10.1177/1081286519883674

Cited by 10 publications

(3 citation statements)

References 46 publications

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“…Great progress has been made in recent times in analyzing methods of solution, as, for example, in Refs. [11][12][13][14], where important new insights have been obtained on Lamb's problem for an elastic half-space. The method of solution consists in using Green functions for the elastic wave equation with combinations of Stokes solutions for double-couple elastic forces.…”

Section: P S M Smentioning

confidence: 99%

Seismological Problem, Seismic Waves and the Seismic Mainshock

Apostol

2023

Mathematics

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The elastic wave equation with seismic tensorial force is solved in a homogeneous and isotropic medium (the Earth). Spherical-shell waves are obtained, which are associated to the primary P and S seismic waves. It is shown that these waves produce secondary waves with sources on the plane surface of a half-space, which have the form of abrupt walls with a long tail, propagating in the interior and on the surface of the half-space. These secondary waves are associated to the seismic mainshock. The results, previously reported, are re-derived using Fourier transformations and specific regularization procedures. The relevance of this seismic motion for the ground motion, the seismographs’ recordings and the effect of the inhomogeneities in the medium are discussed.

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Section: P S M Smentioning

confidence: 99%

Seismological Problem, Seismic Waves and the Seismic Mainshock

Apostol

2023

Mathematics

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“…Emami and Eskandari-Ghadi [36] presented a history of this problem, from its earlier stages to more recent research, by outlining and discussing the various rigorous approaches and methods of solving that have been suggested so far.…”

Section: Introductionmentioning

confidence: 99%

Research of Dynamic Processes in an Anvil During a Collision with a Sample

Pyryev

Penkul

Cybula

2023

Acta Mechanica Et Automatica

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The paper concerns modelling the dynamics of the contact system of the tested sample with an elastic half-space (anvil) during their collision. The original elements in the paper include the proposed general approach to solving the problem of contact dynamics. The presented approach consists in determining the force of impact on the sample during the collision and the joint solution of the problem for the tested sample and the problem for an elastic semi-space under the conditions of the assumptions of Hertz’s theory. The resulting interaction forces allow the determination of displacements and stresses.

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“…The elastic vibration problem caused by a surface or buried vibration source is the basis of the study of the dynamic interaction between structure and soil. [1][2][3][4][5][6][7][8][9][10] It has important theoretical significance and engineering application value in the fields of seismic engineering, geotechnical engineering and geophysics, etc., and hence, is widely investigated. [11][12][13][14][15][16] In 1904, Lamb 17 solved the dynamic Boussinesq problem due to a surface source for an elastic medium.…”

Section: Introductionmentioning

confidence: 99%

Three‐dimensional fundamental solution for unsaturated transversely isotropic half‐space under surface time‐harmonic load

Wang

Zhou

et al. 2023

Num Anal Meth Geomechanics

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An analytical solution of unsaturated poroelastic transversely isotropic (TI) half‐space under surface time‐harmonic load with consideration of compressibility, viscous and inertial coupling of soil skeleton, pore‐water and pore‐air, as well as the capillary pressure is investigated in this paper. Firstly, the governing equations of unsaturated TI soil are established in cylindrical coordinate system. Then, the displacement function and operator theory are introduced to decouple the general solution. Secondly, Fourier expansion and Hankel transform are applied to the circumferential and radial coordinates, and the integral general solutions of soil skeleton displacement, pore‐water displacement and pressure, pore‐air displacement and pressure, and the total stress components are derived in the transformed domain. Combined with boundary conditions and continuity conditions, the fundamental solution of unsaturated TI half‐space is obtained. Finally, the proposed solution is verified by benchmarking with two existing solutions. The influence of the TI parameters, vibration frequency and the degree of saturation on the dynamic response of unsaturated poroelastic half‐space is investigated.

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Lamb’s problem: a brief history

Cited by 10 publications

References 46 publications

Seismological Problem, Seismic Waves and the Seismic Mainshock

Seismological Problem, Seismic Waves and the Seismic Mainshock

Research of Dynamic Processes in an Anvil During a Collision with a Sample

Three‐dimensional fundamental solution for unsaturated transversely isotropic half‐space under surface time‐harmonic load

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