QUASI-3D ANALYTIC MODEL FOR FREE VIBRATION ANALYSIS OF SIMPLY SUPPORTED FUNCTIONALLY GRADED PLATES (SS-FGP)
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Date
2023-03-09
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Abstract
This paper uses a quasi-3D shear deformation theory accounting
for integral terms and including the stretching effect to study the free vibration
of FG plates with simply supported edges. A new function shape is used to
show the variation of tangential stresses through the z-direction of the plate.
Poisson’s ratio is supposed to be constant, but Young’s modulus and densities
are assumed to be graded in the thickness direction according to the power
law function. The present plate theory satisfies the zero tension on the upper
and lower surfaces of the FG plate without using shear correction factors. The
equations of motion are obtained via Hamilton’s principle and solved using
Navier’s solution type. The present natural frequencies correspond with the
ones in many publications; the outcomes of geometrical ratio, side to thickness ratio, and the material index on the natural frequencies of SS-FGP are
investigated.