Free vibration characteristics of sectioned unidirectional/bidirectional functionally graded material cantilever beams b
- PDF / 1,328,719 Bytes
- 18 Pages / 612 x 792 pts (letter) Page_size
- 41 Downloads / 256 Views
APPLIED MATHEMATICS AND MECHANICS (ENGLISH EDITION) 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 WANG2,3
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 Apr. 23, 2020 / Revised Jul. 19, 2020)
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. Key words finite element model (FEM), dynamics, functionally graded material (FGM), Timoshenko beam theory Chinese Library Classification O321 2010 Mathematics Subject Classification
1
70J10, 74K10, 74H45
Introduction
Functionally graded materials (FGMs) are advanced material systems characterized by progressively varying properties, which allow them to be used in a wide range of engineering ∗ Citation: VIET, N. V., ZAKI, W., and WANG, Q. Free vibration characteristics of sectioned unidirectional/bidirectional functionally graded material cantilever beams based on finite element analysis. Applied Mathematics and Mechanics (English Edition) (2020) https://doi.org/10.1007/s10483-020-2664-8 † Corresponding author, E-mail: [email protected] Project supported by Khalifa University of Science and Technology (No. CIRA 2019-024) ©The Author(s) 2020
2
N. V. VIET, W. ZAKI, and Quan WANG
applications[1] . In particular, FGMs can be designed to meet specific requirements in terms of corrosion resistance, weight reduction, toughness, strength, wear resistance and heat isolation, etc. These requirements may be needed in extreme environments such as in nuclear power generation[2], aerospace applications[3] , engines[4–5] , and b
Data Loading...
