Free vibrations of a stiffened cylindrical shell

Abstract

This report presents the first stage of an investigation of the response to random noise of a stiffened cylinder, representing an aircraft fuselage, including an analysis of the lower modes of such a cylinder. Preliminary investigations suggested that assumptions and approximations which are valid for the uniform, i.e., unstiffened, shell are not necessarily valid for a shell with heavy stiffening, and this report therefore starts with a review of existing theories in which the assumptions are examined critically, and, it is hoped, somewhat rationalised. There is very little literature on stiffened shells and this review deals mainly with uniform ones, including the general analysis of strain in a thin shell and the vibrations of a uniform cylindrical shell in vacuo, but includes some comments on the effects of an acoustic medium round the shell. The energy approach is then extended to give the resonant frequencies and natural modes of a circular cylindrical shell uniformly stiffened with closely spaced longerons and frames, 'close spaced' implying that stiffener spacing is much less than the spacing of nodal lines. The effects of rotary inertia have had to be included owing to the lack of symmetry of the section about the skin, but shear deflections are still neglected. Further numerical work is required before much comment can be made on tile results, but they seem to be similar in nature to those obtained for the uniform cylinder. Finally, some indication is given of how the theory can be extended to cover higher-order modes where shear deflection and stiffener spacing become important.