One-Dimensional vs. Three-Dimensional Models in Free Vibration Analysis of Axially Functionally Graded Beams with Non-Uniform Cross-Sections

Abstract

A comparison of one-dimensional (1D) and three-dimensional (3D) models for simulating free vibrations of axially functionally graded material (AFGM) beams with non-uniform cross-sections was carried out. Both models were constructed using ABAQUS and the eigenvalue problem was solved to determine the natural frequencies and their corresponding mode shapes. User-defined material model subroutines (UMAT) were developed using 1D beam or 3D hexagonal graded finite elements to implement material gradients into appropriate finite element models. The performance of both models was evaluated using data for beams with non-uniform cross-sections and material gradation profiles for which natural frequencies were available in the literature. The accuracy and effectiveness of each modeling approach proposed were estimated by comparing the results obtained. Generally, distinctions between the 1D and 3D models become more pronounced as the geometric complexity and material inhomogeneity of AFGM beams increases, especially for high-frequency modes.