Analysis of Natural Frequency of Reinforced Multi-Layered Isotropic Cylindrical Shell with Three Rings under External Pressures Based on FSDT

This paper presents the study on natural frequency of reinforced multi-layered isotropic cylindrical shells with three rings under external pressures. The multi-layered cylindrical shell is formed by three layers of isotropic where the inner and outer layers are stainless steel and the middle layer is aluminum. The reinforced multi-layered shell equations with three rings and external pressures are established based on first order shear deformation theory (FSDT). The governing equations of motion were employed, using energy functional and by applying the Ritz method. The boundary conditions represented by end conditions of the multi-layered cylindrical shell are simply supported-simply supported (SS-SS), clamped-clamped (C-C) and free-free (F-F). This research was solved with computer programming using MAPLE package. The influence of external pressure, rings position and different boundary conditions on natural frequencies characteristics is studied. The results shows that reinforced rings and external pressures have effect on the natural frequency of multi-layered isotropic cylindrical shell and cause the natural frequency to increase. The results presented can be used as an important benchmark for researchers to validate their analytical methods.