Wave Propagation in Viscoelastic and Poroelastic Continua: A Boundary Element Approach

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Martin Schanz

Wave Propagation in Viscoelastic and Poroelastic Continua

A Boundary Element Approach

Martin Schanz

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English

Springer-Verlag Berlin and Heidelberg GmbH & Co. K
08 May 2001

Differential calculus & equations; Analytical mechanics

Series: Lecture Notes in Applied and Computational Mechanics

Wave propagation in poroelastic and viscoelastic solids treated by the Boundary Element method in time domain is the topic of this research book. A novel boundary element formulation has been presented based on the Convolution Quadrature Method. Because in this time-stepping formulation only Laplace domain fundamental solutions are needed this method can be effectively applied to a plenty of problems, e.g. , anisotropic or transversely isotropic continua. So, this method combines the advantage of the Laplace domain with the advantage of a time domain calculation. Here, wave propagation phenomenon in viscoelastic as well as poroelastic half spaces are considered. The Rayleigh wave as well as the slow compressional wave in the poroelastic solid is discussed.

By: Martin Schanz
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Country of Publication: Germany
Edition: 2001 ed.
Volume: 2
Dimensions: Height: 235mm, Width: 155mm, Spine: 12mm
Weight: 970g
ISBN: 9783540416326
ISBN 10: 3540416323
Series: Lecture Notes in Applied and Computational Mechanics
Pages: 170
Publication Date: 08 May 2001
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

1. Introduction.- 2. Convolution quadrature method.- 2.1 Basic theory of the convolution quadrature method.- 2.2 Numerical tests.- 3. Viscoelastically supported Euler-Bernoulli beam.- 3.1 Integral equation for a beam resting on viscoelastic foundation.- 3.2 Numerical example.- 4. Time domain boundary element formulation.- 4.1 Integral equation for elastodynamics.- 4.2 Boundary element formulation for elastodynamics.- 4.3 Validation of proposed method: Wave propagation in a rod.- 5. Viscoelastodynamic boundary element formulation.- 5.1 Viscoelastic constitutive equation.- 5.2 Boundary integral equation.- 5.3 Boundary element formulation.- 5.4 Validation of the method and parameter study.- 6. Poroelastodynamic boundary element formulation.- 6.1 Biot’s theory of poroelasticity.- 6.2 Fundamental solutions.- 6.3 Poroelastic Boundary Integral Formulation.- 6.4 Numerical studies.- 7. Wave propagation.- 7.1 Wave propagation in poroelastic one-dimensional column.- 7.2 Waves in half space.- 8. Conclusions — Applications.- 8.1 Summary.- 8.2 Outlook on further applications.- A. Mathematic preliminaries.- A.1 Distributions or generalized functions.- A.2 Convolution integrals.- A.3 Laplace transform.- A.4 Linear multistep method.- B. BEM details.- B.1 Fundamental solutions.- B.1.1 Visco- and elastodynamic fundamental solutions.- B.1.2 Poroelastodynamic fundamental solutions.- B.2 “Classical” time domain BE formulation.- Notation Index.- References.