Fluids and Periodic Structures

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.