JOURNAL OF LIAONING TECHNICAL UNIVERSITY

EFFECT OF WINKLER VARIABLE AND PASTERNAK ELASTIC FOUNDATIONS ON THE FREE VIBRATION OF FUNCTIONALLY GRADED MATERIAL PLATE.

MAROUF Omar, BENDAHANE Khaled, BOUGUENINA Otbi, SEHOUL Mohammed, BELAKHDAR Khalil

Abstract-

Elastic foundations are widely used to study the behavior of structures under loads such as bending, buckling, and vibration. The aim of this paper is to study the free vibration of functionally graded plates (FGP) resting on a variable elastic foundation, using the refined theory of plates with four unknowns, without the need for a shear correction factor. The elastic foundation is assumed to be a two-parameter Pasternak-Winkler, with a variety of the Winkler layer along one side of the plate, but the Pasternak layer is constant. The originality of this paper lies in the analysis of the effect of a variable elastic foundation on the free vibrations of the FGP. To demonstrate the accuracy of this approach, numerical comparisons were made between the present formulation and those in the literature. The results are very good. Finally, new results are presented to show the effect of the Winkler variety. The results show that variations in the modulus of the Winkler foundation have a considerable effect on the natural frequency.

Key words: elastic foundations effect, free vibration, functionally graded plate, refined plate theory, Winkler variation.