Membrane Motion of a Thin,Single Layer,Generally Orthotropic,Cylindrical Shell

A membrane theory for thin, single layer, generally orthotropic, cylindrical shells experiencing harmonic, axi-symmetric motion is established. Shear-coupling in the plane of the middle surface of the shell results in coupled motion occurring in three dispersive modes of propagation. Long and short wavelength velocity limits in the three modes are analogous to those of an isotropic shell, however, the short wavelength limits are reversed in the first and second modes. Three discrete frequencies occur for which: (1). motion is predominantly radial; (2). motion becomes uncoupled in the first and second modes; (3). the type of wave changes from extension-shear to shear-extension (or vise-versa) for most off-angle orientations. These events occur within the range of wavelengths, established in the membrane theory for isotropic shells, which render the theory accurate. When the shell is specially orthotropic, the in-plane motion is uncoupled; the first mode is a non-dispersive shear mode, while the second and third are dispersive extensional modes.