The Effect of Intermediate Ring Support on the Vibration Behavior of Functionally Graded Conical Shells

In this study, the free vibrational behavior of a thin-walled functionally graded conical shell with intermediate ring support is investigated. Theoretical formulations were established based on the first-order shear deformation theory. The governing equations of motion were solved using the Galerkin method. Applying a set of displacement functions, the equations of motion result in an eigenvalue problem, by solving which, the natural frequencies of vibration are determined. Material properties are assumed to be varied in the thickness direction according to the power-law volume fraction function. It has been attempted to examine the effects of ring support position on the natural frequencies of vibration and to introduce the optimal scenarios of the support placement to achieve a higher frequency. In addition, a 3D FE model was built in the ABAQUS CAE software in order to validate the results of the analytical model. The analytical results were in close agreement with the literature and also the numerical ones. Moreover, the effects of some commonly used end conditions, variations in the shell geometrical parameters, changes in the ring support placement have been investigated on the vibrational behavior.