Abstract
Abstract In this work, we study vibrations of three-layered cylindrical shells with one ring support along its length. Nature of material of the central layer is a functionally graded material (FGM) type. The considered FGM is of stainless steel and nickel. The internal and external layers are presumed to be made of isotropic material i.e., aluminum. The functionally graded material composition of the center layer is assorted by three volume fraction laws (VFL) which are represented by mathematical expressions of polynomial, exponential and trigonometric functions. The implementation of Rayleigh-Ritz method has been done under the Sanders’ shell theory to obtain the shell frequency equation. Natural frequencies (NFs) are attained for the present model problem under six boundary conditions. Use of characteristic beam functions is made for the estimation of the dependence of axial modals. The impact of layer material variations with ring support is considered for many ring positions. Also the effect of volume fraction laws is investigated upon vibration characteristics. This investigation is performed for various physical parameters. Numerous comparisons of values of shell frequencies have been done with available models of such types of results to verify accuracy of the present formulation and demonstrate its numerical efficiency.
Highlights
In this work, we study vibrations of three-layered cylindrical shells with one ring support along its length
Material properties of the isotropic material as well as functionally graded material (FGM) constituents are given in reference [1] and [2]
The frequency analysis of three-layered FGM cylindrical shell is performed to determine the effect of ring support
Summary
Abstract: In this work, we study vibrations of three-layered cylindrical shells with one ring support along its length. A FG shell was done by Arshad et al [14] with effect of This material variation yields a variety of frequency specdifferent fraction laws by applying Love’s first order shell tra Stability of these shells is solidified by ring supports theory. Arshad et al [17] ex- to examine the influence of ring supports at different posiplored vibration properties of bi-layered cylinder-shaped tions along the shell length. A cylindrical coordinate θ analyzed vibration behavior of the tri-layered FGM circular cylinders They employed the Ritz method and used the Love’s shell theory. Vibration frequencies are analyzed for three along the length layered cylindrical shells These shells are assembled from three layers assuming that the central is made of function- scribed below: ally graded materials, internal and external layers remain isotropic type of materials.
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