MAA MPP Model

The Maa microperforate model determines the characteristic impedence \((Z_{c})\) of the layer based on the perforate diameter \((d)\), center-to-center distance \((b)\), and thickness \((t)\).

Unlike other material models, the Maa MPP model does not calculate a characteristic wavenumber \((k_{c})\). Instead, a separate transfer matrix is used.

Determination of Characteristic Impedence

\[ Z_{c} = r+j\omega m \]

where \(r\) is:

\[ r = \frac{32\eta t}{\phi d^2} r_{1} \]

\[ r_{1} = \sqrt{1+\frac{x^2}{32}}+\frac{\sqrt{2}}{32} x \frac{d}{t} \]

\(m\) is:

\[ m = \frac{\rho_{0}t}{\phi} m_{1} \]

\[ m_{1} = 1+\frac{1}{\sqrt{1+\frac{x^2}{2}}}+\frac{0.85d}{t} \]

and

\[ x = \frac{d}{2}\sqrt{\frac{\omega\rho_{0}}{\eta}} \]

\[ \phi = \frac{\pi}{4}\Bigg(\frac{d}{b}\Bigg)^2 \]

The characteristic impedence \((Z_{c})\) is then used directly in the layer transfer matrix via the Add_MAA_MPP_Layer method.

Model Parameters:

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

\[ d = \Bigg[m\Bigg]\tag{perforate diameter} \]

\[ b = \Bigg[m\Bigg]\tag{center-to-center distance} \]

\[ t = \Bigg[m\Bigg]\tag{layer thickness} \]

Defining Other Symbols:

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

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

\[ \eta = \Bigg[Pa*s\Bigg]\tag{viscosity of air} \]

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