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.
Highlights
Graded materials (FGMs) are composite materials made of a mixture of at least two base materials with a continuous variation of their volumetric fraction in accordance with a prescribed function
A parametric study is performed to investigate the influence of different parameters on the natural frequencies of functionally graded materials (FGM) cylindrical shells
The accuracy and efficacy of the proposed approach are examined by comparing the present results of the free vibration of FGM cylindrical shells with other results published in previous studies
Summary
Graded materials (FGMs) are composite materials made of a mixture of at least two base materials with a continuous variation of their volumetric fraction in accordance with a prescribed function. Shahbaztabar et al [38] investigated the free vibrations of FGM cylinders implanted into a Pasternak elastic foundation, based on the first-order shear deformation theory and the Rayleigh-Ritz method. Liu et al [26] investigated the free vibrations characteristics of FGM circular cylinders based on the first-order shear deformation shell theory. Najafizadeh and Isvandzibaei [29] studied the free vibration of FGM thin cylindrical shells with ring supports using third-order shear deformation theory (TSDT), and the governing equations were obtained using an energy functional with the Rayleigh-Ritz method. An analysis of a FGM closed circular cylindrical shell is performed using the higher-order shear deformation shell theory and the virtual displacements principle in a strong form based on the collocation of radial basis functions. Parametric studies are performed for FGM cylindrical shells considering several boundary conditions in order to show the effect of several design variables on the natural frequencies
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