Natural frequencies analysis of functionally graded circular cylindrical shells

Abstract

In the present work, a study on natural frequencies of functionally graded materials (FGM) circular cylindrical shells is presented. TheFGM is considered to be a mixture of two materials. The volumetric fractions are considered to vary in the radial direction (i.e., through the thickness) in compliance with a conventional power-law distribution. The equivalent material properties are estimated based on the Voigt model. The analysis of the FGM cylindrical shells is performed using the third-order shear deformation shell theory and the principle of virtual displacements. Moreover, the third-order shear deformation shell theory coupled with Carrera’s unified formulation is applied for the derivation of the governing equations associated with the free vibration of circular cylindrical shells. The accuracy of this method is examined by comparing the obtained numerical results with other previously published results. Additionally, parametric studies are performed for FGM cylindrical shells with several boundary conditions in order to show the effect of several design variables on the natural frequencies such as the power-law exponent, the circumferential wave number, the length to radius ratio and the thickness to radius ratio.

Natural Frequencies Optimization of Thin-Walled Circular Cylindrical Shells Using Axially Functionally Graded Materials

“…This trend differs from that of FGM cylinders when material constituents vary in thickness (z). In the case of material variations in thickness, the natural frequencies of the FGM thin cylindrical shells are limited between the natural frequencies of the first-and second-base materials [31,37]. The natural frequencies depend on material distributions through the axial direction of FGM circular cylindrical shells.…”

“…Liu et al [36] used FSDT and wave function expansions to find the natural frequencies. Alshabatat and Zannon [37] studied the free vibrations of FGM cylindrical shell by employing third-order shear deformation theory and Carrera's unified formulation. All previous studies on materials' volume fraction variations in the radial direction of cylindrical shells (i.e., through thickness) based on simple power law [29][30][31]34,35,37], exponential law [30,31], trigonometric law [30,31], and four-parameter power laws [32,33,36].…”