Analytical solution for free vibration of stiffened functionally graded cylindrical shell structure resting on elastic foundation

In this work, the analytical solution for free vibration of functionally graded cylindrical shell with stiffeners resting on Winkler-Pasternak foundation with several boundary conditions is reported. Material properties of the cylindrical shell are assumed to be varying smoothly and continuously across the thickness according to the power law distribution of the volume fraction of constituents. The governing equations of the stiffened functionally graded cylindrical shell resting on elastic foundation are obtained by using Hamilton's principle, the first-order shear deformation theory and the Lekhnitsky smeared stiffeners technique. The purpose of the present study is to illustrate a simple approach to get the natural frequency of the stiffened functionally graded cylindrical shell with several boundary conditions by using the Galerkin method with beam functions of the axial displacement fields. A good agreement is obtained as the present results in comparison with those of publications in the existing literature. In numerical investigations, some influences of volume fraction index, cylindrical shell's geometric ratios, boundary conditions and elastic foundation parameters on the fundamental frequency of the stiffened cylindrical shell resting on elastic foundation are given.