Free vibration of functionally graded open cylindrical shells based on several refined higher order displacement models

Abstract

Free vibration analysis of functionally graded (FG) open cylindrical shells is presented here using various refined higher order theories. Present study undertakes the displacement based approach including higher order shear and normal deformation theory (HOSNT) along with first order shear deformation theory (FOST) and higher order shear deformation theory (HSDT) models. Difficulty of obtaining three dimensional (3D) solutions and errors associated with classical shell theory (CST) necessitates the requirement of higher order models. Present study takes into account moderately thick shells unlike CST, by considering square of ratio of thickness to radius of shell less than unity, instead of the classical assumption of considering ratio of thickness to radius less than unity. Here Navier method of solution with double trigonometric functions for displacement terms is used to analytically reduce the given set of partial differential equations (PDEs) to an eigenvalue problem. Results are computed using MATLAB and comparison between various higher order models is discussed based on the consideration of middle surface displacement parameters. Present results should establish benchmark solutions for free vibration analysis of isotropic/orthotropic FG cylindrical panels. Functionally graded material properties are graded according to power law variation in thickness direction. Various shell solutions, based on other theories and 3D solutions available in the literature are compiled along with present solutions.