Top

Published in:

2024 | OriginalPaper | Chapter

A Dynamic Green’s Function for the Homogeneous Viscoelastic and Isotropic Half-Space

Authors : Tsviatko V. Rangelov, Petia S. Dineva, George D. Manolis

Published in: New Trends in the Applications of Differential Equations in Sciences

Publisher: Springer Nature Switzerland

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

A dynamic 3D Green’s function for the homogeneous, isotropic and viscoelastic (of the Zener type) half-space is derived in a closed form. The results obtained here can be used as either stand-alone solutions for simple problems or in conjunction with a boundary integral equation formulations to account for complex boundary conditions. In the later case, mesh-reducing boundary element formulations can be constructed as an alternative method for numerical implementation purposes.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Definite/Indefinite Integrals Involving Non-integral Powers for Certain Trigonometric Functions Times Special Functions

next chapter Area and Perimeter Full Distribution Functions for Planar Poisson Line Processes and Voronoi Diagrams

Dineva, P., Manolis, G., Wuttke, F.: Fundamental solutions in 3d elastodynamics for the bem: A review. Eng. Anal.Bound. Elem. 105, 47–69 (2019)

Dominguez, J.: Boundary Elements in Dynamics. Computational Mechanics Publications, Southampton (1993)

Eringen, A.C., Suhubi, E.S.: Elasto–dynamics. vol. 2: Linear Theory. Academic Press, New York (1975)

Johmson, L.R.: Green‘s function for lamb‘s problem. Geophys. J. Int. 37(1), 99–131 (1974)

Kausel, E.: Fundamental Solutions in Elastodynamics: A Compendium. Cambridge University Press, Cambridge (2006)

Lamb, H.: On the propagation of tremors over the surface of an elastic solid. Philos. Trans. R. Soc. London A 203, 1–42 (1904)

Mainardi, F.: Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematicam Models. Imperial College Press, London, UK (2010)

Makrou, A.A., Manolis, G.D.: A fractional derivative zener model for the numerical simulation of base isolated structures. Bull. Earthquake Eng. 14(1), 283–295 (2016)

Manolis, G.D., Dineva, P.S., Rangelov, T.V., Wuttke, F.: Seismic Wave Propagation in Non–Homogeneous Elastic Media by Boundary Elements. Solid Mechanics and its Applications, v. 240, Springer Int. Publ., Cham, Switzerland (2017)

10.

Manolis, G.D., Shaw, R.: Green’s function for a vector wave equation in mildly heterogeneous continuum. Wave Motion 24, 59–83 (1996)

11.

Midlin, R.D.: Waves and vibrations in isotropic, elastic plates. In: J.N. Goodier, N.J. Hoff (eds.) Structural Mechanics. Pergamon Press, New York (1960)

12.

Pak, R.Y.S.: Asymmetric wave propagation in an elastic half-space by a method of potentials. J. Appl. Mech. 54(1), 121–126 (1995)

13.

Rangelov, T.V., Dineva, P.S., Manolis, G.D.: Dynamic response of a cracked viscoelastic anisotropic plane using boundary elements and fractional derivatives. J. Theor. Appl. Mech. 48(2), 24–49 (2018)

14.

Tadeu, A., Antonio, J., Godinho, L.: Green‘s function for two and a half dimensional elastodynamic problems in a half-space. Comput. Mech. 27, 484–491 (2001)

15.

Vladimirov, V.: Equations of Mathematical Physics. Marcel Dekker, Inc., New York (1971)

16.

Yuan, H., Pan, Z.: Discussion on the time-harmonic elastodynamic half-space green‘s function obtained by superposition. Math. Probl. Eng. ID 2717810, 1–7 (2016)

17.

Zhang, C., Gross, D.: On Wave Propagation in Elastic Solids with Cracks. Comput. Mech. Publ., Southampton (1998)

Title: A Dynamic Green’s Function for the Homogeneous Viscoelastic and Isotropic Half-Space
Authors: Tsviatko V. Rangelov
Petia S. Dineva
George D. Manolis
Publisher: Springer Nature Switzerland
Book: New Trends in the Applications of Differential Equations in Sciences
Print ISBN: 978-3-031-53211-5

Electronic ISBN: 978-3-031-53212-2

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-3-031-53212-2_13

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"