Resistive Screen Model

The Resistive Screen model implemented in acoustipy is from the paper below, neglecting the frame mechanical properties:

Mathieu Gaborit, Olivier Dazel, Peter Göransson; A simplified model for thin acoustic screens. J. Acoust. Soc. Am. 1 July 2018; 144 (1): EL76–EL81. https://doi.org/10.1121/1.5047929

The equations for the dynamic mass density \((\tilde{\rho})\) and dynamic bulk modulus \((\widetilde{K})\) can be found below:

\[ \tilde{\rho} = \frac{\rho_{0}}{\phi}+\frac{\sigma}{j{\omega}} \]

\[ \widetilde{K} = \frac{P_{0}}{\phi} \]

The Add_Resistive_Screen method then converts The dynamic mass density and bulk modulus to the characteristic impedence \((Z_{c})\) and wavenumber \((k_{c})\) for use in the layer transfer matrix.

\[ Z_{c} = \sqrt{\tilde{\rho}\widetilde{K}} \]

\[ k_{c} = {\omega}\sqrt{\frac{\tilde{\rho}}{\widetilde{K}}} \]

Model Parameters:

Using the following nomenclature --- Symbol = [Units] (name)

\[ \sigma = \Bigg[\frac{Pa*s}{m^2}\Bigg]\tag{static airflow resistivity} \]

\[ \phi = \Bigg[unitless\Bigg]\tag{porosity} \]

Defining Other Symbols:

Using the following nomenclature --- Symbol = [Units] (name) or Symbol = equation = [Units] (name)

\[ \rho_{0} = \Bigg[\frac{kg}{m^3}\Bigg]\tag{air density} \]

\[ \omega = 2{\pi}f = \Bigg[\frac{radians}{s}\Bigg]\tag{angular frequency} \]