A Homogenisation Procedure for the Free Vibration Analysis of Functionally Graded Beams at Large Vibration Amplitudes
The purpose of the present paper is to show that the problem of geometrically nonlinear free vibrations of functionally graded beams (FGB) with immovable ends can be reduced to that of isotropic homogeneous beams with effective bending stiffness and axial stiffness parameters by using an homogenization procedure. The material properties of the functionally graded composites examined are assumed to be graded in the thickness direction and estimated through the rule of mixture. The theoretical model is based on the Euler-Bernouilli beam theory and the Von Kármán geometrical nonlinearity assumptions. Hamilton’s principle is applied and a multimode approach is derived to calculate the fundamental nonlinear frequency parameters, which are found to be in a good agreement with the published results. The non-dimensional curvatures associated to the nonlinear fundamental mode are also given for various vibration amplitudes in the case of clamped-clamped FGB.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1088860Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1489
 M. Simsek, Nuclear Engineering and Design, 240 (2010).
 J. Murín, M. Aminbaghai, V. Kuti, Engineering Structures, 32 (2010).
 A.E. Alshorbagy, M.A. Eltaher, F.F. Mahmoud, Applied Mathematical Modelling, 35 (2011).
 S.M.R. Khalili, A.A. Jafari, S.A. Eftekhari, Composite Structures, 92 (2010).
 S. Kapuria, M. Bhattacharyya, A.N. Kumar, Composite Structures, 82 (2008)C. J. Kaufman, Rocky Mountain Research Lab., Boulder, CO, private communication, May 1995.
 Z. Yu , F. Chu, Journal of Sound and Vibration, 325 (2009).
 A. Fallah, M.M. Aghdam, European Journal of Mechanics - A/Solids, 30 (2011).
 L. Azrar, R. Benamar, R.G. White, Journal of Sound and Vibration, 224 (1999).