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

doi:10.1007/s10483-020-2664-8

Applied Mathematics and Mechanics (English Edition) ›› 2020, Vol. 41 ›› Issue (12): 1787-1804.doi: https://doi.org/10.1007/s10483-020-2664-8

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

N. V. VIET¹, W. ZAKI¹, Quan WANG^2,3

1. Department of Mechanical Engineering, Khalifa University of Science and Technology, Abu Dhabi 127788, United Arab Emirates;
2. Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, Guangdong Province, China;
3. Department of Civil and Environmental Engineering, Shantou University, Shantou 515063, Guangdong Province, China

收稿日期:2020-04-23 修回日期:2020-07-19 发布日期:2020-11-21
通讯作者: W. ZAKI E-mail:wael.zaki@ku.ac.ae
基金资助:
Project supported by Khalifa University of Science and Technology (No. CIRA 2019-024)

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

N. V. VIET¹, W. ZAKI¹, Quan WANG^2,3

1. Department of Mechanical Engineering, Khalifa University of Science and Technology, Abu Dhabi 127788, United Arab Emirates;
2. Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, Guangdong Province, China;
3. Department of Civil and Environmental Engineering, Shantou University, Shantou 515063, Guangdong Province, China

Received:2020-04-23 Revised:2020-07-19 Published:2020-11-21
Contact: W. ZAKI E-mail:wael.zaki@ku.ac.ae
Supported by:
Project supported by Khalifa University of Science and Technology (No. CIRA 2019-024)

摘要/Abstract

摘要： 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 onedimensional (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 the Timoshenko or Euler-Bernoulli beam theory. 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.

关键词: finite element model (FEM), dynamics, functionally graded material (FGM), Timoshenko beam theory

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 onedimensional (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 the Timoshenko or Euler-Bernoulli beam theory. 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.

Key words: finite element model (FEM), dynamics, functionally graded material (FGM), Timoshenko beam theory

中图分类号:

N. V. VIET, W. ZAKI, Quan WANG. Free vibration characteristics of sectioned unidirectional/bidirectional functionally graded material cantilever beams based on finite element analysis[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(12): 1787-1804.

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

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

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