Free Vibration Characteristics of Shell Roofs

The equation of motion of cylindrical shells is written using Donnell-Karman-Jenkins (DKJ) theory; and a Levy-type solution is used for computing their natural frequencies and model shapes. The method is applicable to shells simply supported on rigid traverses on the curved edges which have arbitrary support conditions along the longitudinal edges. Five cases of characteristic roots arise depending on the value of the natural frequency. Complete expressions for forces and displacements are presented for all the cases. The method has been used to compute the natural frequencies of a shell simply supported on all edges. Values are obtained that are identical with those obtained by the Navier type solution. A shell with edge beams has been analyzed. Its frequencies observed on a reinforced concrete shell roof model have been compared with theoretical values and found to agree closely.