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On the high-temperature free vibration analysis of elastically supported FGM plates under mechanical in-plane force via GDQR

[+] Author and Article Information
Roshan Lal

Department of Mathematics, IITR, Roorkee 247667, India
rlatmfma@iitr.ac.in

Rahul Saini

Department of Mathematics, IITR, Roorkee 247667, India
rahulsainiiit@gmail.com

1Corresponding author.

ASME doi:10.1115/1.4043489 History: Received December 09, 2018; Revised April 09, 2019

Abstract

In this article, the effect of Pasternak foundation on free axisymmetric vibration of functionally graded circular plates subjected to mechanical in-plane force and a non-linear temperature distribution along the thickness direction has been investigated on the basis of classical plate theory. The plate material is graded in thickness direction according to a power-law distribution and its mechanical properties are assumed to be temperature-dependent. At first, the equation for thermo-elastic equilibrium and then equation of motion for such a plate model have been derived by Hamilton's principle. Employing generalized differential quadrature rule, the numerical values of thermal displacements and frequencies for clamped and simply supported plates vibrating in the first three modes have been computed. Values of in-plane force parameter for which the plate ceases to vibrate have been reported as critical buckling loads. The effect of temperature difference, material graded index, in-plane force and foundation parameters on the frequencies has been analyzed. The benchmark results for uniform and linear temperature distributions have been computed. A study for plates made with the material having temperature-independent mechanical properties has also been performed as a special case. Comparison of results with the published work has been presented.

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