Large Vibration Amplitude of Circular Functionally Graded Plates Resting on Pasternak Foundations

Authors: El Kaak Rachid, El Bikri Khalid, Benamar Rhali

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 was studied. The material properties of the functionally graded composites examined were 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 shearing foundations is to decrease the frequency ratio, where it increases with the effect of the nonlinear foundation stiffness. 

Keywords: Non-linear vibrations, Circular plates, Pasternak foundation, functionally graded materials.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1087800

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