Asymptotic expansions for wavenumbers in orthotropic fluid-filled circular cylindrical shells for intermediate fluid loading

Coupled wavenumbers in infinite fluid-filled isotropic and orthotropic cylindrical shells are considered. Using the Donnell-Mushtari (DM) theory for thin shells, compact and elegant asymptotic expansions for the wavenumbers are found at an intermediate fluid loading for both the coupled rigid-duct modes ("fluid-originated") and the coupled structural wavenumbers ("structure-originated modes") over the entire frequency range where DM theory is valid. The coupled rigid-duct expansions are found to be valid for O(1) orthotropy and for all circumferential orders, whereas the coupled structural wavenumber expansions are valid for small orthotropy and for low circumferential orders. These two above results are then used to derive the expansions for a set of multiple complex roots that display a locking behavior at this intermediate fluid-loading. The expansions are matched with the numerical solutions of the coupled dispersion relation and the match is found to be good over most of the frequency range.