Journal article
Effective acoustic equations for a two-phase medium with microstructure
Mathematical and computer modelling, Vol.39(13), pp.1431-1448
2004
Handle:
https://hdl.handle.net/2376/107683
Abstract
We study acoustic wave propagation in a two-phase medium in which the solid phase is a linear elastic material, and the fluid phase is assumed to be a compressible Newtonian barotropic fluid. Assuming that properties of the medium change rapidly on the small scale ε, we analyze the microscopic nonlinear Navier-Stokes equations and show that they can be linearized when ε tends to zero. Using a variant of Tartar's method of oscillating test functions, we derive effective acoustic equations which turn out to be viscoelastic. In order to treat disordered materials occurring in nature, we develop a new approach to describing geometry of a nonperiodic medium with length scale separation. Our approach is not based on probabilistic considerations. Instead, we postulate that certain inequalities hold uniformly on the microscale.
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Details
- Title
- Effective acoustic equations for a two-phase medium with microstructure
- Creators
- R.P Gilbert - Department of Mathematical Sciences University of Delaware Newark, DE 19716, U.S.AA Panchenko - Department of Mathematics Washington State University Pullman, WA 99164, U.S.A
- Publication Details
- Mathematical and computer modelling, Vol.39(13), pp.1431-1448
- Academic Unit
- Mathematics and Statistics, Department of
- Publisher
- Elsevier Ltd
- Identifiers
- 99900546954401842
- Language
- English
- Resource Type
- Journal article