Semi-analytical evaluation of integral forms associated with Lamb's problem

Guenfoud, Salah; Amrane, Mohamed Nadir; Босаков, С. В.; Ouelaa, Nouredine

doi:10.1016/j.soildyn.2008.04.007

Cited by 7 publications

(2 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…According to Guenfoud et al [16], the displacements of the half-space surface with inertial properties due to the action of a uniformly distributed load on a rectangle element with dimensions b c × (Fig. 5) ( )…”

Section: Problem Approachmentioning

confidence: 99%

Dynamic analysis of a beam resting on an elastic half-space with inertial properties

Guenfoud

Босаков

Laefer

2009

Soil Dynamics and Earthquake Engineering

Self Cite

View full text Add to dashboard Cite

This work gives a semi-analytical approach for the dynamic analysis of beams and plates resting on an elastic half-space with inertial properties. Such calculations have been associated with significant mathematical challenges, often leading to unrealizable computing processes. Therefore, this paper presents a detailed analysis of Green's function defining surface displacements of such a space in the contact zone with structures, which allows determination of reactive forces and other physical responses. The obtained solutions can be applied to (i) study dynamic interaction between soil and structures, (ii) determine transient wave fields caused by a seismic source, and (iii) assess numerical computations with different numerical methods programs. Natural frequencies, natural shapes, and the dynamic response of a beam due to external harmonic excitation are determined.Eigenfrequencies and Eigenshapes are presented. Validation with a Boussinesq problem illustrates the inertia effect on the results of the dynamic analysis.

show abstract

Section: Problem Approachmentioning

confidence: 99%

Dynamic analysis of a beam resting on an elastic half-space with inertial properties

Guenfoud

Босаков

Laefer

2009

Soil Dynamics and Earthquake Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…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.

View full text Add to dashboard Cite

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.

show abstract

Evaluation of the integrals of Green’s function of Lamb’s model used in contact problems

Gherdaoui¹,

Guenfoud²,

Босаков

et al. 2020

Acta Mech

View full text Add to dashboard Cite

Semi-analytical evaluation of integral forms associated with Lamb's problem

Cited by 7 publications

References 14 publications

Dynamic analysis of a beam resting on an elastic half-space with inertial properties

Dynamic analysis of a beam resting on an elastic half-space with inertial properties

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

Evaluation of the integrals of Green’s function of Lamb’s model used in contact problems

Contact Info

Product

Resources

About