Green's function for tangentialy loaded horizontaly layered half-space

Tomaž Pliberšek (Author), Andrej Umek (Author)

Abstract

V članku je obravnavan nov pristop k evaluaciji integralne predstavitve Greenove funkcije za slojevit pol-prostor, ki je na površini obremenjen s harmonično tangencialno točkovno silo. Enačbe gibanja razvežemo z uvedbo valovnih potencialov. Nevezane enačbe rešujemo tako, da jih s pomočjo predpostavljene odvisnosti od kotne koordinate in uvedbo Hanklove transformacije, pretvorimo v navadne diferencialne enačbe. Njihova rešitev in uvedba inverzne Hanklove transformacije vodita do integralne predstavitve za pomike na površini pol-prostora. Te nato izvrednotimo s pomočjo predlaganega tristopenjskega postopka. Najprej integrande razcepimo na dva dela, od katerih prvi po izvedeni integraciji vodi do singularnih pomikov, drugi del pa do regularnega dela pomikov. Opazimo, da je ta drugi del, potem ko uvedemo ustrezno izbrane razvejiščne reze in veljavnost integrandov s pomočjo analitičnega nadaljevanja razširimo s pozitivne realne osi Hanklovega parametra na njegovo celotno kompleksno ravnino, možno izvrednotiti s pomočjo konturne integracije za poljubno število slojev. Tako je ta del pomikov podan z rezidui integranda izvrednotenih v njegovih polih in integrali s končno razdaljo integracije vzdolž razvejiščih rezov. Te slednje z lahkoto izvrednotimo z zaželeno natančnostjo s pomočjo numerične integracije Izbrani numerični rezultati dopolnjujejo matematična izvajanja.

Keywords

elastodynamics;elastic wave propagation;Green`s function;horizontaly layered half-space;horizontal point load;

Data

Language:	English
Year of publishing:	2008
Typology:	1.01 - Original Scientific Article
Organization:	UM FGPA - Faculty of Civil Engineering, Transportation Engineering and Architecture
UDC:	624.131:51
COBISS:	12399638
ISSN:	1854-0171
Parent publication:	Acta geotechnica Slovenica
Views:	744
Downloads:	64
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary title:	Greenova funkcija tangencialno obremenjenega horizontalno slojevitega polprostora
Secondary 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.
Secondary keywords:	elastodinamika;valovanje;Greenova funkcija;horizontalno slojevit polprostor;tangencialna koncentrirana sila;
URN:	URN:SI:UM:
Type (COBISS):	Scientific work
Pages:	str. 50-69
Volume:	ǂVol. ǂ5
Issue:	1
Chronology:	2008
ID:	10939520