Open Access

ARTICLE

Three-Dimensional Free Vibration Analysis of Sandwich FGM Cylinders with Combinations of Simply-Supported and Clamped Edges and Using the Multiple Time Scale and Meshless Methods

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Computers, Materials & Continua 2015, 46(1), 17-56. https://doi.org/10.3970/cmc.2015.046.017

Abstract

An asymptotic meshless method using the differential reproducing kernel (DRK) interpolation and multiple time scale methods is developed for the three-dimensional (3D) free vibration analysis of sandwich functionally graded material (FGM) circular hollow cylinders with combinations of simply-supported and clamped edge conditions. In the formulation, we perform the mathematical processes of nondimensionalization, asymptotic expansion and successive integration to obtain recurrent sets of motion equations for various order problems. Classical shell theory (CST) is derived as a first-order approximation of the 3D elasticity theory, and the motion equations for higher-order problems retain the same differential operators as those of CST, although with different nonhomogeneous terms. Expanding the primary field variables of each order as the Fourier series functions in the circumferential direction, and interpolating these in the axial direction using the DRK interpolation, we can obtain the leading-order solutions of this analysis. The higher-order modifications can be obtained in a systematic manner, in which the solvability and normality conditions are used to eliminate secular terms and uniquely determine these modifications. Some 3D solutions of the natural frequencies of sandwich FGM cylinders and their corresponding through-thickness distributions of modal variables are given to demonstrate the performance of the asymptotic DRK-based meshless method.

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Keywords

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