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1.
Green's function for tangentialy loaded horizontaly layered half-space
Tomaž Pliberšek, Andrej Umek, 2008, original scientific article

Abstract: The topic of this paper is a novel evaluation of the integral representation of the surface Greenćs function for a layered half-space, loaded on its surface by a harmonic tangential point force. The equations of motions are reduced to wave equations by the introduction of wave potentials. The Hankel transform is applied to them and they are consecutively solved leading to the integral representation of surface displacements. They are consecutively evaluated by the proposed three step procedure. First the singularity is extracted. It is further noted that so obtained integrals, after suitably chosen branch cuts and analytic continuation of integrands are introduced, can be evaluated by contour integration for an arbitrary number of layers. They are, therefore, expressed by number of residues at the poles of integrand and the integrals along finite portions of the branch cuts. The latter ones can easily be evaluated to any desired accuracy leading to a closed form solution. Some numerical results corroborating the presented approach are given.
Keywords: elastodynamics, elastic wave propagation, Green`s function, horizontaly layered half-space, horizontal point load
Published in DKUM: 05.06.2018; Views: 1191; Downloads: 82
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2.
Innovative solution principles of wave problems in horizontaly layered medias
Andrej Štrukelj, Andrej Umek, Tomaž Pliberšek, 2006, original scientific article

Abstract: The paper presents engineeringly reasonable transformation of surface displacements of horizontally layered half-space. The latter shows in the half-space present types of waves. It is shown that surface waves are expressed through residuums in poles of the integrand and the volume waves are expressed as integrals along corresponding branch cuts. The singularity which always appears in the basic singular solution in elastodynamics is in this case exactly excluded. In the second part of the paper the behaviour of Stonely waves is investigated in greater detail. It is shown that in the case of layers of finite thickness their appearance and velocities depends not onlyon the material characteristics of neighbouring layers but also on their thickness.
Keywords: geomechanics, horizontally layered halfspace, volume waves, surface waves, Green`s function, Stonely waves
Published in DKUM: 17.05.2018; Views: 1398; Downloads: 108
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3.
Green's function for an elastic layer loaded harmonically on its surface
Tomaž Pliberšek, Andrej Štrukelj, Andrej Umek, 2005, original scientific article

Abstract: The Green's function in surface displacement plays an important role in soil structure interaction. In evaluating the Green's function, several difficulties occur because it is formulated in the infinite integral form. This paper outlines a method of analyzing the steady-state dynamic response of an elastic layer subjected to general point load excitation. It is assumed that the load is applied at the surface. The application Hankel integral transform, to the governing differential equations and boundary conditions yields the response displacements at the surface in integral representation. It will be shown that these semi-infinite integrals can be reduced to the integral with the finite range of integration, which can be efficiently taken numerically. The numerical results are presented, which show the efficiency of the developed procedure.
Keywords: civil engineering, geomechanics, soil-structure interaction, layered halfspace, Green's function, elastodynamics
Published in DKUM: 15.05.2018; Views: 1444; Downloads: 91
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4.
On the solvability of second-order impulsive differential equations with antiperiodic boundary value conditions
Yepeng Xing, Valery Romanovski, 2008, original scientific article

Abstract: We prove existence results for second-order impulsive differential equations with antiperiodic boundary value conditions in the presence of classical fixed point theorems. We also obtain the expression of Green's function of related linear operator in the space of piecewise continuous functions.
Keywords: second-order impulsive differential equations, antiperiodic boundary value conditions, Green's function
Published in DKUM: 26.06.2017; Views: 1260; Downloads: 399
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5.
Approximate expressions for the Green's functions of a semi-infinite, elastic medium
Tomaž Pliberšek, Andrej Umek, 2010, original scientific article

Abstract: On the basis of an exact, discretized presentation of the Green's function components, their closed-form approximations are developed. Their accuracy is considered to be better than the tolerances in the intrusive measurements data for the identification of the mechanical characteristics of soils. The use of these approximate expressions is believed to considerably reduce the computational effort in soil-structure interaction problems and open up new possibilities for the non-intrusive identification of soils.
Keywords: elastodynamics, half-space, Green's function, approximate solutions
Published in DKUM: 31.05.2012; Views: 2029; Downloads: 114
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6.
Evaluation of Green`s function for vertical point-load excitation applied to the surface of a semi-infinite elastic medium
Andrej Štrukelj, Tomaž Pliberšek, Andrej Umek, 2006, original scientific article

Abstract: The topic of this paper is to show that the integrals of infinite extent representing the surface displacements of a layered half-space loaded by a harmonic, vertical point load can be reduced to integrals with finite integration range. The displacements are first expressed through wave potentials and the Hankel integral transform in the radial coordinate is applied to the governing equations and boundary conditions, leading to the solutions in the transformed domain. After the application of the inverse Hankel transform it is shown that the inversion integrands are symmetric/antimetric in the transformation parameter and that this characteristic is preserved for any number of layers. Based on this fact the infinite inversion integrals are reduced to integrals with finite range by choosing the suitable representation of the Bessel function and use of the fundamental rules of contour integration, permitting simpler analytical or numerical evaluation. A numerical example is presented and the results are compared to those obtained by the CLASSI program.
Keywords: civil engineering, soil mechanics, Green`s function, layered half-space, vertical point load
Published in DKUM: 31.05.2012; Views: 2293; Downloads: 40
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