acdecom.WaveGuide.get_psi_circular

WaveGuide.get_psi_circular(m, n, r, phi, **kwargs)

Return the normalized mode shapee of the (m,n)-mode for a circular duct. Modes are normalized to be orthonormal, see WaveGuide.get_c().

\[\Psi_{mn} = \frac{J_m(R\kappa_{mn}) \mathbf{e}^{\mathbf{i} m \phi}}{C_{mn}}\]

where \(\kappa\) is the eigenvalue, see WaveGuide.get_eigenvalue() .

Parameters

• m (int) – Mode-order in the circumferential direction. The plane wave has the order 0.

• n (integer) – Mode-order in the radial direction. The plane wave has the order 0.

• r (float or array_like) – Radial-coordinate.

• phi (float or array_like) – Circumferential-coordinate.

• kwargs (additional arguments) –

Returns

The normalized mode shapee of the (m,n)-mode at position (pos1,pos2).

Return type

complex