Free vibration characteristics of sectioned unidirectional/bidirectional functionally graded material cantilever beams based on finite element analysis

N. V. Viet, W. Zaki, Quan Wang

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

Advancements in manufacturing technology, including the rapid development of additive manufacturing (AM), allow the fabrication of complex functionally graded material (FGM) sectioned beams. Portions of these beams may be made from different materials with possibly different gradients of material properties. The present work proposes models to investigate the free vibration of FGM sectioned beams based on one-dimensional (1D) finite element analysis. For this purpose, a sample beam is divided into discrete elements, and the total energy stored in each element during vibration is computed by considering either Timoshenko or Euler-Bernoulli beam theories. Then, Hamilton’s principle is used to derive the equations of motion for the beam. The effects of material properties and dimensions of FGM sections on the beam’s natural frequencies and their corresponding mode shapes are then investigated based on a dynamic Timoshenko model (TM). The presented model is validated by comparison with three-dimensional (3D) finite element simulations of the first three mode shapes of the beam.

Original languageBritish English
Pages (from-to)1787-1804
Number of pages18
JournalApplied Mathematics and Mechanics (English Edition)
Volume41
Issue number12
DOIs
StatePublished - Dec 2020

Keywords

  • 0321
  • dynamics
  • finite element model (FEM)
  • functionally graded material (FGM)
  • Timoshenko beam theory

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