Frequency analysis of tetra layered FGM cylindrical shell with S-S Edge condition

A Cylindrical shell consists of a curved surface that extends around a central axis, with its thickness being relatively small compared to its height and radius. It has wide range applications in pressure vessels and tanks, heat exchangers, aerospace etc. This article analyzes four shell surfaces, the first and third layers of functionally graded material, and the second and fourth layers of isotropic material. The natural frequency is influenced by several thick layers. The shell frequency equation is obtained by usig the Rayleigh-Ritz approach. The strain and curvature-displacement relations are derived from Sander's shell theory. Characteristic beam functions are employed to assess the dependence of axial modal and trigonometric volume fraction law is used to attain the vibration anaylsis. Results are acquired for different thickness-to-radius and length-to-radius ratios under various edge conditions. For simply supported edge circumstances, the natural frequencies are calculated by using MATLAB software.