Generalized Asymptotic Expansions for the Wavenumbers in Infinite Flexible Circular Cylindrical Shells in the Intermediate Frequency Ranges

摘要

In this paper, we find valid complex asymptotic expansions for all the wavenumbers in infinite flexible in vacuo circular cylindrical shells. The cylindrical shell is modeled using the Donnell-Mushtari thin shell theory. Using regular and singular perturbation methods, expansions for wavenumbers are found over a wide frequency range. However, the novelty of this work lies in extending the work available in the current literature by finding expansions in the intermediate frequency range (around &!=1) where the shell dynamics is most interesting. The non-dimensional thickness parameter~2 of the shell is used as the asymptotic parameter and the solutions are obtained as a function of~2, the non-dimensional frequency &!, the circumferential order n and Poisson's ratio 1/2. The results are compared with the numerical solutions of the dispersion relations and a good match is obtained.