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Wave Propagation in Viscoelastic and Poroelastic Continua: A Boundary Element Approach 2001 ed. [Kõva köide]

  • Formaat: Hardback, 170 pages, kõrgus x laius: 235x155 mm, kaal: 970 g, X, 170 p., 1 Hardback
  • Sari: Lecture Notes in Applied and Computational Mechanics 2
  • Ilmumisaeg: 08-May-2001
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540416323
  • ISBN-13: 9783540416326
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  • Formaat: Hardback, 170 pages, kõrgus x laius: 235x155 mm, kaal: 970 g, X, 170 p., 1 Hardback
  • Sari: Lecture Notes in Applied and Computational Mechanics 2
  • Ilmumisaeg: 08-May-2001
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540416323
  • ISBN-13: 9783540416326
Wave propagation is an important topic in engineering sciences, especially, in the field of solid mechanics. A description of wave propagation phenomena is given by Graff [ 98]: The effect of a sharply applied, localized disturbance in a medium soon transmits or 'spreads' to other parts of the medium. These effects are familiar to everyone, e.g., transmission of sound in air, the spreading of ripples on a pond of water, or the transmission of radio waves. From all wave types in nature, here, attention is focused only on waves in solids. Thus, solely mechanical disturbances in contrast to electro-magnetic or acoustic disturbances are considered. of waves - the compression wave similar to the In solids, there are two types pressure wave in fluids and, additionally, the shear wave. Due to continual reflec­ tions at boundaries and propagation of waves in bounded solids after some time a steady state is reached. Depending on the influence of the inertia terms, this state is governed by a static or dynamic equilibrium in frequency domain. However, if the rate of onset of the load is high compared to the time needed to reach this steady state, wave propagation phenomena have to be considered.
Introduction
1(6)
Convolution quadrature method
7(16)
Basic theory of the convolution quadrature method
7(4)
Numerical tests
11(12)
Series expansion of the test functions f1 and f2
12(2)
Computing the integration weights ωn
14(4)
Numerical convolution
18(5)
Viscoelastically supported Euler-Bernoulli beam
23(16)
Integral equation for a beam resting on viscoelastic foundation
23(10)
Fundamental solutions
24(3)
Integral equation
27(6)
Numerical example
33(6)
Fixed-simply supported beam
33(4)
Fixed-free viscoelastic supported beam
37(2)
Time domain boundary element formulation
39(18)
Integral equation for elastodynamics
40(4)
Boundary element formulation for elastodynamics
44(2)
Validation of proposed method: Wave propagation in a rod
46(11)
Influence of the spatial and time discretization
47(6)
Comparison with the ``classical'' time domain BE formulation
53(4)
Viscoelastodynamic boundary element formulation
57(20)
Viscoelastic constitutive equation
57(4)
Boundary integral equation
61(3)
Boundary element formulation
64(2)
Validation of the method and parameter study
66(11)
Three-dimensional rod
67(4)
Elastic foundation on viscoelastic half space
71(6)
Poroelastodynamic boundary element formulation
77(28)
Biot's theory of poroelasticity
78(4)
Elastic skeleton
78(2)
Viscoelastic skeleton
80(2)
Fundamental solutions
82(4)
Poroelastic Boundary Integral Formulation
86(7)
Boundary integral equation
86(5)
Boundary element formulation
91(2)
Numerical studies
93(12)
Influence of time step size and mesh size
93(5)
Poroelastic half space
98(7)
Wave propagation
105(30)
Wave propagation in poroelastic one-dimensional column
105(19)
Analytical solution
105(6)
Poroelastic results
111(8)
Poroviscoelastic results
119(5)
Waves in half space
124(11)
Rayleigh surface wave
124(7)
Slow compressional wave in poroelastic half space
131(4)
Conclusions - Applications
135(8)
Summary
135(2)
Outlook on further applications
137(6)
A. Mathematic preliminaries 143(8)
Distributions or generalized functions
143(3)
Convolution integrals
146(1)
Laplace transform
147(1)
Linear multistep method
148(3)
B. BEM details 151(6)
Fundamental solutions
151(3)
Visco- and elastodynamic fundamental solutions
151(1)
Poroelastodynamic fundamental solutions
152(2)
``Classical'' time domain BE formulation
154(3)
Notation Index 157(2)
References 159(10)
Index 169