Using the higher-order shear deformation theory to analyze the free vibration of stiffened rotating FGM conical shells in a thermal environment: Fid-Bau Portal

Using the higher-order shear deformation theory to analyze the free vibration of stiffened rotating FGM conical shells in a thermal environment

Aris, Hamid / Ahmadi, Habib

Abstract

Abstract In this paper, free vibration analysis of rotating stiffened truncated conical shells with functionally graded materials (FGM) in a thermal environment is presented based on the higher-order shear deformation theory (HSDT). Assuming Coriolis acceleration and the centrifugal force, the governing equations of stiffened rotating FGM truncated conical shells are extracted utilizing the HSDT, the Donnell kinematics assumptions, and the smeared stiffeners technique. The partial differential equations are discretized into a set of ordinary differential equations employing Galerkin’s approach. The characteristic equation is computed as a tenth-order polynomial equation in terms of natural circular frequency. Regarding the characteristic equation, the free vibration of the stiffened rotating shell is analyzed to investigate the natural circular frequency. The results are presented and compared with the latest pertained developments found in the literature. Also, the effects of the internal and external stiffener, volume-fraction index, temperature changes, and different vertex angles on the frequency response curve are examined for various rotating speeds.

Highlights • The HSDT and smeared stiffeners approach are utilized in the modeling. • The effect of hoop tension, due to the centrifugal force is considered. • Galerkin’s approach is used to discretize the PDEs to a set of ODEs. • The characteristic equation is computed as a tenth-order polynomial equation. • The natural frequency $ω$ increases by increasing the semi-vertex angle $δ$ and rotation $Ω$ .