Asymptotic wavenumber expansions of a strongly orthotropic fluid-filled circular cylindrical shell

In this paper, a suitable nondimensional ‘orthotropy parameter’ is defined and asymptotic expansions are found for the wavenumbers in in vacuo   and fluid-filled orthotropic circular cylindrical shells modeled by the Donnell–Mushtari theory. Here, the elastic moduli in the two directions are greatly different; the particular case of Ex≫EθEx≫Eθ is studied in detail, i.e., the elastic modulus in the longitudinal direction is much larger than the elastic modulus in the circumferential direction. These results are compared with the corresponding results for a ‘slightly orthotropic’ shell (Ex≈EθEx≈Eθ) and an isotropic shell. The novelty of this presentation lies in obtaining closed-form expansions for the in vacuo and coupled wavenumbers in an orthotropic shell using perturbation methods aiding in a better physical understanding of the problem.

► Asymptotic expansions are found for wavenumbers in an infinite orthotropic shell.
► Donnell–Mushtari shell theory has been used.
► Strong orthotropy with a large difference between ExEx and EyEy is studied.
► In vacuo and fluid-filled shells are studied.