Fluids and periodic structures
Author(s)
Bibliographic Information
Fluids and periodic structures
（Research in applied mathematics）
Wiley, c1995
- : Wiley
- : Masson
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Note
Bibliography: p 321-328. - Includes index
Description and Table of Contents
Description
The main emphasis of this book lies in understanding the vibrations of fluid-solid structures, in which mechanical bodies interact with a surrounding fluid. Deriving models representing these vibrations and validating them are principal aims, as is the study of their asymptotic behaviour. For the last 20 years or so, homogenization methods have proved to be powerful tools for studying such heterogeneous media. Some of the classical ones today are multiple scale expansions and energy methods and its variants. The authors introduce here a non-standard homogenization technique and apply it to the class of eigenvalue problem alluded to above. It is based on the so-called Bloch wave decomposition, a technique that is often used in physics. This volume also includes a systematic presentation of two-scale convergence analysis which is a mdoern approach to treat homogenization problems.
Table of Contents
- Part 1 Elements of spectral theory with examples: some function spaces and their properties
- some classical examples of vibrating systems
- spectral theory of linear operators
- effects of perturbations. Part 2 Spectral problems in fluid-solid structures: mathematical models of vibrations in fluid-solid structures
- existence results
- bounds on eigenvalue
- numerical methods in fluid-solid structures. Part 3 Asymptotic methods in fluid-solid structures: Beppo-Levi spaces and their properties
- Bloch wave method in a classical example
- Bloch wave method in the Laplace model
- Bloch wave method in the Helmhlotz model
- two-scale convergence method
- asymptoptic expansions in fluid-solid structures
- open questions.
by "Nielsen BookData"