Last modified: 2013-05-04
Abstract
In the present study, the problem of geometrically nonlinear free vibrations of functionally graded circular plates (FGCP) resting on Pasternak elastic foundation with immovable ends is studied. An homogenization procedure (HP) has been developed to reduce the problem under consideration to that of isotropic homogeneous circular plate. 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 classical Plate 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 dealing with the problem of functionally graded plates. On the other hand, the influence of the foundation parameters on the nonlinear frequency to the linear frequency ratio of the FGCP has been studied. The effect of the linear and the shearing foundations is to decrease the frequency ratio, whereas the effect of the nonlinear foundation stiffness is to increase it.
References
1-A. Allahverdizadeh, M.H. Naei, M. Nikkhah Bahrami, Nonlinear free and forced vibration analysis of thin circular functionally graded plates, Journal of Sound and Vibration 310 (2008) 966–984.
2- A. Zerkane, K. El Bikri and R. Benamar, "A homogenization procedure for nonlinear free vibration analysis of functionally graded beams resting on nonlinear elastic foundations”, Applied Mechanics and Materials Journal (accepted-2011).
3- M. Haterbouch, R. Benamar, The effects of large vibration amplitudes on the axisymmetric mode shapes and natural frequencies of clamped thin isotropic circular plates, part II: iterative and explicit analytical solution for non-linear coupled transverse and in-plane vibrations, Journal of Sound and Vibration 277 (2004) 1–30.
4- C.L.D. Huang, I.M. Al-Khattat, Finite amplitude vibrations of a circular plate, International Journal of Nonlinear Mechanics 12
(1977) 297–306.
5- X.-L. Huang, H.-S. Shen, Nonlinear vibration and dynamic response of functionally graded plates in thermal environment, International Journal of Solids and Structures 41 (9–10) (2004) 2403–2427
6- Hui-Shen Shen,Functionally graded materials : nonlinear analysis of plates and shells. Taylor & Francis Group, LLC. 2009