Transverse shear and normal deformation effects on vibration behaviors of functionally graded micro-beams
- PDF / 275,519 Bytes
- 18 Pages / 612 x 792 pts (letter) Page_size
- 2 Downloads / 214 Views
APPLIED MATHEMATICS AND MECHANICS (ENGLISH EDITION) https://doi.org/10.1007/s10483-020-2662-6
Transverse shear and normal deformation effects on vibration behaviors of functionally graded micro-beams∗ Zhu SU1,† , Lifeng WANG1 , Kaipeng SUN2 , Jie SUN2 1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; 2. Shanghai Institute of Satellite Engineering, Shanghai 201109, China (Received May 17, 2020 / Revised Jul. 13, 2020)
Abstract A quasi-three dimensional model is proposed for the vibration analysis of functionally graded (FG) micro-beams with general boundary conditions based on the modified strain gradient theory. To consider the effects of transverse shear and normal deformations, a general displacement field is achieved by relaxing the assumption of the constant transverse displacement through the thickness. The conventional beam theories including the classical beam theory, the first-order beam theory, and the higherorder beam theory are regarded as the special cases of this model. The material properties changing gradually along the thickness direction are calculated by the Mori-Tanaka scheme. The energy-based formulation is derived by a variational method integrated with the penalty function method, where the Chebyshev orthogonal polynomials are used as the basis function of the displacement variables. The formulation is validated by some comparative examples, and then the parametric studies are conducted to investigate the effects of transverse shear and normal deformations on vibration behaviors. Key words quasi-three dimensional theory, modified strain gradient theory, functionally graded (FG) micro-beam, size effect, vibration, general boundary condition Chinese Library Classification O321, O327 2010 Mathematics Subject Classification 74H45, 70J10
1
Introduction
As advanced composite materials, functionally graded (FG) materials possess distinctive features of gradually spatial changes in the material properties, which enable FG materials to avoid the stress concentration of conventional laminated composite materials. Besides, FG materials can satisfy the multi-functional requirements by a wide selection of material constituents. ∗ Citation: SU, Z., WANG, L. F., SUN, K. P., and SUN, J. Transverse shear and normal deformation effects on vibration behaviors of functionally graded micro-beams. Applied Mathematics and Mechanics (English Edition) (2020) https://doi.org/10.1007/s10483-020-2662-6 † Corresponding author, E-mail: [email protected] Project supported by the National Natural Science Foundation of China (Nos. 51805250 and 11602145), the Natural Science Foundation of Jiangsu Province of China (No. BK20180429), the China Postdoctoral Science Foundation (No. 2019M660114), and the Jiangsu Planned Projects for Postdoctoral Research Funds of China (No. 2019K054) c
The Author(s) 2020
2
Zhu SU, Lifeng WANG, Kaipeng SUN, and Jie SUN
Consequently, FG materials are suitable for many engineering fields and c
Data Loading...
