Free vibration analysis of a transversely stiffened circular thin hollow cylinder made of functionally graded materials (FGMs) is analytically evaluated. Functionally graded materials are inhomogeneous composites which are usually made from a mixture of metal and ceramic. The gradient compositional variation of the constituents from one surface to the other provides an elegant solution to the problem of high transverse shear stresses induced when two dissimilar materials with large differences in material properties are bonded. In this paper, application of an FGM made of two different materials is investigated by applying Ritz method. While cylinder is assumed to be thin, strain energy evaluation is performed by Sander’s theorem. Stiffeners which are not necessarily in the same uniform shape are treated as discrete elements and can be placed on both sides of the cylinder or concentrate in the middle wall. Bending, stretching and wrapping effects of stiffeners are considered in calculation of strain energy. Evaluation of kinetic energy of stiffeners is performed by taking into account rotary and translational inertia. To apply Ritz method, polynomial functions are used and natural frequencies and mode shapes of ring stiffened thin cylinder are investigated. Results are compared and verified with previous theoretical and experimental studies of stiffened thin cylinders. Comparison indicates a good agreement between results.
Strain Energy Density Prediction of Mixed-Mode Crack Propagation in Functionally Graded Materials