Frequency analysis of functionally graded bi-layered cylindrical shells with ring support by galerkin technique

Buckling of vibrating cylindrical shells is an important aspect in aerospace and defense engineering. The proposed study is conducted to craving a method which is easier but still authentic for predicting the natural frequencies (Hz) of bi-layered cylindrical shells with ring support. The ring support is placed arbitrarily along the axis of the shell. It is assumed that the layers of the shell have a uniform thickness. Both layers are contrived independently by functionally graded technique having the constituents, stainless steel, and nickel. The material properties of the com- ponents of functionally graded layers are supervised by volume fraction power-law distribution and assumed to vary continuously and smoothly throughout the thickness of the layers. By interchanging the position of FGM constituents four kinds of cylindrical shells are formulated and its influence on frequency characteristics are analyzed. The expression for strain and curvature–displacement relationships are obtained by utilizing Love’s first approximation of linear thin shell theory. Simply supported end conditions are imposed on edges. For numerical approximations, the Galerkin approach is employed to formulate the frequency equation in the form of the eigenvalue problem. The variation in frequency for various shell parameters as; length, height, radius, the width of layers material constituents and the position of the ring supports position are discussed. Effectiveness, validity, and accuracy of the present methodology has proven by comparing the evaluated numerical results with the results available in the open literature.