Analytical and Numerical Investigation of Vibration Characteristics in Shear-Deformable FGM Beams

Abstract

In this study, the free vibration characteristics of a functionally graded (FG) shear-deformable Timoshenko beam were investigated both analytically and numerically. The work is notable for its significant contribution to the literature, particularly in addressing analytically challenging problems related to complex FGM structures using advanced computer-aided finite element methods. For the analytical approach, the governing equations and associated boundary conditions were derived using Hamilton’s principle of minimum potential energy. These equations were then solved using the Navier solution method to determine the natural frequencies of the beam. In the numerical analysis, a 3D FG beam model was developed in the ABAQUS finite element software (2023, Dassault Systèmes, Providence, RI, USA)using the second-order hexahedral (HEX20/C3D20) and 1D three-node quadratic beam (B32) elements. The material gradation was defined layer-by-layer along the thickness direction in accordance with the rule of mixtures. Modal analysis was subsequently performed to extract the natural frequency values. The results show a high level of agreement between the analytical and numerical solutions. and were consistent with previously published studies in the literature.