Calculations of modes in circumferentially nonuniform lined ducts.

This paper proposes a computationally efficient method of determining eigenfunctions and eigenvalues of acoustic modes propagating in circular lined ducts with zero or uniform flow. Linings with circumferentially nonuniform impedance, as found in nacelle acoustics, are the focus. The method of solution adapts in two important respects--the presence of flow and the imposition of impedance boundary conditions--the series expansion method first proposed by Pagneux et al. [J. Acoust. Soc. Am. 110, 1307-1314 (2001)] to calculate the eigenvalues of Lamb modes. The inclusion of flow, and a corresponding different method of solution leading to an improved convergence of eigenvalues (O(N(-5)), N is the truncation of radial basis of expansion), is the important new feature as compared to the previous adaptation by Bi et al. [J. Acoust. Soc. Am. 122, 280-291 (2007)]. As a result, it becomes possible to safely determine and in a simple manner the eigenvalues and eigenfunctions of circumferentially nonuniform lined ducts in the presence of uniform flow, up to relatively high frequencies (e.g., 30