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Wave Propagation in Viscoelastic and Poroelastic Continua [electronic resource] : A Boundary Element Approach / by Martin Schanz

Author:
Schanz, Martin, 1963-
Published:
Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2001.
Edition:
1st ed. 2001.
Physical Description:
X, 170 pages : online resource
Additional Creators:
SpringerLink (Online service)
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Contents:
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.
Summary:
In this book, a numerical method to treat wave propagation problems in poroelastic and viscoelastic media is developed and evaluated. The method of choice is the Boundary Element Method (BEM) since this method implicitly fulfills the Sommerfeld radiation condition. The crucial point in any time-dependent BEM formulation finding time-dependent fundamental solutions is overcome employing the Convolution Quadrature Method. This quadrature rule makes it possible to establish a boundary element time-stepping procedure based on the known Laplace domain fundamental solutions for viscoelastic and poroelastic continua. Using this method, e.g., tremors produced by earthquakes or machines can be pre-calculated and subsequent buildings prevented from such disturbances.
Subject(s):
ISBN:
9783540445753
Digital File Characteristics:
PDF
text file
Part Of:
Springer Nature eBook
View MARC record | catkey: 34518674