Finite element models in Lamb’s problem

Kravtsov, A. V.; Kuznetsov, S. V.; Sekerzh–Zen’kovich, S. Ya.

doi:10.3103/s002565441106015x

Cited by 39 publications

(9 citation statements)

References 11 publications

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“…In the transient setting, numerical solutions to the Lamb problem for elastic media were considered in [28], using the finite-element method for plane and spatial problems for the case of harmonic loading and in [29], using the finite-difference method for the plane problem for the case of distributed loading on the free surface.…”

Section: Introductionmentioning

confidence: 99%

The discrete Lamb problem: Elastic lattice waves in a block medium

Aleksandrova

2014

Wave Motion

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Highlights• An asymptotic behavior of perturbations for the transient Lamb problem for a point step load in a discrete medium is obtained.• Numerical examples are given to demonstrate the accuracy of our analytical solutions.• AbstractWe study the propagation of transient waves under the action of a vertical step point load on the surface of a half-space filled by a block medium. The block medium is modeled by a square lattice of masses connected by springs in the directions of the axes x, y, and in the diagonal directions. The problem is solved by two methods. Analytically, we obtain asymptotic solutions in the vicinity of the Rayleigh wave at large time intervals. Numerically, we obtain a solution for any finite time interval. We compare these solutions with each other and with the solution to the Lamb problem for an elastic medium.

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Section: Introductionmentioning

confidence: 99%

The discrete Lamb problem: Elastic lattice waves in a block medium

Aleksandrova

2014

Wave Motion

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“…They are associated with the numerical solution of the external Lamb problem, in which it is possible to obtain the necessary Rayleigh wave, Fig. 5a, [23,39,40]; or consider the solution of a more complex internal Lamb problem, in which, along with the Rayleigh wave, it is possible to simulate the propagation of the head SP wave, see Fig. 5b [27].…”

Section: Mathematical Models For the Study Of Vertical Barriersmentioning

confidence: 99%

Seismic Barriers for Protection Against Surface and Headwaves: Multiple Scatters and Metamaterials

2021

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“…By applying the integral transform method and the inverse transformation technique, exact solution for a two-dimensional Lamb's problem due to a strip impulse loading in elastic media was presented [6]. The details for solving Lamb's problem using finite element method were explored (Kravtsov, 2011) [7]. The efficiency and accuracy of integration operation were studied (Guenfoud, 2009;Arcos, 2013) [8,9].…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution for 2D and 3D Lamb Problem in Saturated Soil Incorporating Effects of Compressibility of Solid and Pore Fluid

2021

Teh. vjesn.

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In this paper, to avoid the complexity, a simple and efficient analytical solution is derived for both 2D and 3D Lamb problems, respectively, in saturated soil under harmonic excitations. Unlike the existing solutions, the proposed solutions for both 2D and 3D Lamb problems in saturated soil under harmonic excitation are capable of well revealing the effect of compressibility of both liquid phase and solid phase on the ground displacements. By applying Fourier transforms and Hankel transforms on the governing equations of wave propagation in saturated soil, wave equations are transformed to ordinary differential equations. Combining the boundary conditions and draining conditions on the ground surface, the displacement solutions on the surface of saturated porous soil due to line and point harmonic excitations are derived, respectively. Then, the solutions in frequency domain are obtained by inverse integral transforms. In the meanwhile, for the sake of discussion without losing its generality, the nondimensional solutions for three-dimensional Lamb problem are derived. The effectiveness and accuracy of the proposed solutions are demonstrated by employing three different approaches. Finally, parametric studies are conducted to investigate the effects of the governing parameters (i.e., exciting frequency, bulk modulus of soil matrix, and bulk modulus of pore fluid) on variation of non-dimensional displacement with the increasing distance away from the excitation source. The results indicate that, in contrast to the effect of the compressibility of soil matrix, the exciting frequency as well as the compressibility of the pore fluid play significant role in affecting the variation of displacement on ground surface subjected to excitations, which particularly highlights that the compressibility of the pore fluid should be carefully considered for evaluating the ground movements.

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Finite element models in Lamb’s problem

Cited by 39 publications

References 11 publications

The discrete Lamb problem: Elastic lattice waves in a block medium

The discrete Lamb problem: Elastic lattice waves in a block medium

Seismic Barriers for Protection Against Surface and Headwaves: Multiple Scatters and Metamaterials

Analytical Solution for 2D and 3D Lamb Problem in Saturated Soil Incorporating Effects of Compressibility of Solid and Pore Fluid

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