FREE VIBRATION MODELING IN A FUNCTIONALLY GRADED HOLLOW CYLINDER USING THE LEGENDRE POLYNOMIAL APPROACH

Abstract

Introduction: The building industry is under increasing pressure to maximize performance while reducing the costs and the environmental impact. To solve this problem, a new type of materials, i.e., functionally graded materials (FGMs), are proposed. These materials have the advantage of being able to withstand harsh environments without losing their properties. Purpose of the study: The paper aims to further extend the understanding of the propagation modes and characteristics of guided waves in FGM cylinders with infinite lengths. In the course of the study, we analyzed a cylindrical shell composed of three annular layers, each separated by a gradient layer across the wall thickness. A modeling tool based on the Legendre orthogonal polynomial method is proposed in the paper. Methods: The method applied results in an eigenvalue/eigenvector problem. The boundary conditions are integrated into the constitutive equations of guided wave propagation. The phase velocity and normalized frequency dispersion curves are calculated. Besides, the displacement distributions and stress field profiles for a functionally graded cylinder with various graded indices in both modes (axisymmetric and symmetric) are calculated and discussed. The results show a constant fluctuation of effective FGM material. Results: It was found that the phase velocity curves of the same mode decrease as the exponents of the power law increase. In addition, the boundary conditions have a greater impact on the normal stresses. The accuracy and effectiveness of the improved orthogonal polynomial method are demonstrated through a comparison of the exact solution obtained by an analytical-numerical method and our numerical results.