Vibration analysis of ring-stiffened cross-ply laminated cylindrical shells

This work presents the formulation of governing equations for a symmetric cross-ply laminated cylindrical shell with a circumferential stiffener. Two kinds of the circumferential stiffeners are considered: outer ring and inner ring. The effects of rotatory inertia and transverse shearing strain of both the cross-ply laminated shell and stiffener are considered. Further, the warping effect of stiffener also is included. An analytic method is presented to obtain the modal frequencies and their corresponding mode shape functions of the ring-stiffened laminated shell. The orthogonality of two distinct sets of mode shape functions is shown. The effects of inner ring and outer ring on modal frequencies of the ring-stiffened laminated shell are compared. Further, the effect of ply arrangement on modal frequencies of the ring-stiffened shell also is studied. The forced vibration of the ring-stiffened laminated shell due to a concentrated transient force is examined. The stress distributions in the plies of the ring-stiffened laminated shell due to the transient force are investigated.