Delany-Bazley-Miki model
The model by Delany-Bazley-Miki [Mik90] consists in revised expressions for the complex wave number $k$ and characteristic impedance $Z_{c}$ of Delany-Bazley model [DB70].
In the case of multiple layers, Miki noticed that the real part of the surface impedance when computed with the originial Delany-Bazley model sometimes becomes negative at low frequencies denoting a non-physical result. From Delany and Bazley measurements data realized 20 years before on fibrous materials with porosities close to 1.00, Miki proposes to use the following expressions for the wave number and characteristic impedance:
|
$Z_{c} = \rho_{0} c_{0}
\Bigg[ 1+5.50 \left(10^3\frac{f}{\sigma}\right)^{-0.632}
- j 8.43 \left(10^3\frac{f}{\sigma}\right)^{-0.632} \Bigg]$ $k = \displaystyle{\frac{\omega}{c_{0}}} \Bigg[ 1 + 7.81 \left(10^3\frac{f}{\sigma}\right)^{-0.618} - j 11.41 \left(10^3\frac{f}{\sigma}\right)^{-0.618} \Bigg]$ |
(1) |
The elapsed time between the original Delany-Bazley model and Miki modifications of it explains, partly, the extensive use of Delany-Bazley expressions although Miki corrections are preferable to use.
The boundaries, proposed by Delany and Bazley, for the validity of their original expressions are:
| $0.01 < \displaystyle{\frac{f}{\sigma}} < 1.00$ | (2) |
Miki takes care not to extrapolate these boudaries even if he had observed his revised expressions are well behaved in a larger frequency range, in particular for $f/\sigma < 0.01$
References
[DB70] Delany M. E. and Bazley E. N.,
Acoustical properties of fibrous absorbent materials, Applied
Acoustics 3, 1970, pp. 105-116
[Mik90] Miki Y.,
Acoustical properties of porous materials - Modifications of
Delany-Bazley models, J. Acoust. Soc. Jpn (E). 11(1), 1990, pp. 19-24
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