scholarly journals Effective Medium Theory for Acoustic Waves in Bubbly Fluids near Minnaert Resonant Frequency

2017 ◽  
Vol 49 (4) ◽  
pp. 3252-3276 ◽  
Author(s):  
Habib Ammari ◽  
Hai Zhang
Keyword(s):  
Resonant Frequency ◽  
Acoustic Waves ◽  
Effective Medium Theory ◽  
Effective Medium ◽  
Medium Theory ◽  
Bubbly Fluids

scholarly journals A proof that multiple waves propagate in ensemble-averaged particulate materials

2019 ◽  
Vol 475 (2229) ◽  
pp. 20190344 ◽  
Author(s):  
Artur L. Gower ◽  
I. David Abrahams ◽  
William J. Parnell
Keyword(s):  
Acoustic Waves ◽  
Volume Fraction ◽  
Effective Medium Theory ◽  
Effective Medium ◽  
Inhomogeneous Material ◽  
Ensemble Averaging ◽  
Reflection And Transmission ◽  
Medium Theory ◽  
Transmission Coefficients ◽  
Cylindrical Inclusions

Effective medium theory aims to describe a complex inhomogeneous material in terms of a few important macroscopic parameters. To characterize wave propagation through an inhomogeneous material, the most crucial parameter is the effective wavenumber . For this reason, there are many published studies on how to calculate a single effective wavenumber. Here, we present a proof that there does not exist a unique effective wavenumber; instead, there are an infinite number of such (complex) wavenumbers. We show that in most parameter regimes only a small number of these effective wavenumbers make a significant contribution to the wave field. However, to accurately calculate the reflection and transmission coefficients, a large number of the (highly attenuating) effective waves is required. For clarity, we present results for scalar (acoustic) waves for a two-dimensional material filled (over a half-space) with randomly distributed circular cylindrical inclusions. We calculate the effective medium by ensemble averaging over all possible inhomogeneities. The proof is based on the application of the Wiener–Hopf technique and makes no assumption on the wavelength, particle boundary conditions/size or volume fraction. This technique provides a simple formula for the reflection coefficient, which can be explicitly evaluated for monopole scatterers. We compare results with an alternative numerical matching method.

Effective medium theory and the attenuation of graphite fiber composites

1993 ◽  
Vol 73 (7) ◽  
pp. 3441-3445 ◽  
Author(s):  
Herbert Überall ◽  
Barbara F. Howell ◽  
Earl L. Diamond
Keyword(s):  
Effective Medium Theory ◽  
Fiber Composites ◽  
Effective Medium ◽  
Graphite Fiber ◽  
Medium Theory

From the Huckel model to effective-medium theory

1991 ◽  
Vol 3 (40) ◽  
pp. 7757-7762 ◽  
Author(s):  
H Hakkinen ◽  
J Mansikka-aho ◽  
M Manninen
Keyword(s):  
Effective Medium Theory ◽  
Effective Medium ◽  
Medium Theory
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