Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories

Thai, Huu-Tai and Vo, Thuc (2012) Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories. International Journal of Mechanical Sciences, 62 (1). 57 - 66. ISSN 0020-7403

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Official URL: http://dx.doi.org/10.1016/j.ijmecsci.2012.05.014

Abstract

In this paper, various higher-order shear deformation beam theories for bending and free vibration of functionally graded beams are developed. The developed theories account for higher-order variation of transverse shear strain through the depth of the beam, and satisfy the stress-free boundary conditions on the top and bottom surfaces of the beam. A shear correction factor, therefore, is not required. In addition, these theories have strong similarities with Euler–Bernoulli beam theory in some aspects such as equations of motion, boundary conditions, and stress resultant expressions. The material properties of the functionally graded beam are assumed to vary according to power law distribution of the volume fraction of the constituents. Equations of motion and boundary conditions are derived from Hamilton's principle. Analytical solutions are presented, and the obtained results are compared with the existing solutions to verify the validity of the developed theories. Finally, the influences of power law index and shear deformation on the bending and free vibration responses of functionally graded beams are investigated.

Item Type: Article
Uncontrolled Keywords: vibration, functionally graded beam, higher-order beam theory, bending
Subjects: H200 Civil Engineering
H300 Mechanical Engineering
H400 Aerospace Engineering
Department: Faculties > Engineering and Environment > Mechanical and Construction Engineering
Depositing User: Thuc Vo
Date Deposited: 28 Aug 2013 08:49
Last Modified: 13 May 2017 15:15
URI: http://nrl.northumbria.ac.uk/id/eprint/13388

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