Effects of uniform interior pressure distribution on vibration of FGM cylindrical shell with rings support based on first-order theory subjected to ten boundary conditions

Abstract

This paper presents the study on natural frequency characteristics of a thin-walled functionally graded material (FGM) cylindrical shell with rings support under symmetric uniform interior pressure distribution. The FGM properties are graded along the thickness direction of the shell. The FGM shell equations with rings support and interior pressure are established based on first-order shear deformation theory. The governing equations of motion were employed, using energy functional and by applying the Ritz method. Ten boundary conditions represented by end conditions of the FGM shell are the following: simply supported-simply supported, clamped-clamped, free-free, clamped-free, clamped-simply supported, free-simply supported, sliding-sliding, sliding-simply supported, sliding-free and sliding-clamped. This problem was solved with computer programming using MAPLE package for numerical investigation. Comparison of the results is carried out to verify the validity of the proposed procedure with published works. The influence of interior pressure, ring support position and number of rings support, and effect of the ten boundary conditions on natural frequency characteristics are studied. The results presented can be used as an important benchmark for researchers to validate their numerical methods when studying natural frequencies of shells with ring and pressure.