Research Papers

On the High-Temperature Free Vibration Analysis of Elastically Supported Functionally Graded Material Plates Under Mechanical In-Plane
Force Via GDQR

[+] Author and Article Information
Roshan Lal

Department of Mathematics,
Roorkee 247667, India
e-mail: rlatmfma@iitr.ac.in

Rahul Saini

Department of Mathematics,
Roorkee 247667, India
e-mail: rahulsainiiit@gmail.com

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received December 9, 2018; final manuscript received April 9, 2019; published online May 17, 2019. Assoc. Editor: Richard Bearee.

J. Dyn. Sys., Meas., Control 141(10), 101003 (May 17, 2019) (12 pages) Paper No: DS-18-1552; doi: 10.1115/1.4043489 History: Received December 09, 2018; Revised April 09, 2019

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 nonlinear temperature distribution (NTD) 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 (TD). 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 (GDQR), 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 (LTDs) have been computed. A study for plates made with the material having temperature-independent (TI) mechanical properties has also been performed as a special case. Comparison of results with the published work has been presented.

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Grahic Jump Location
Fig. 1

Geometrical configuration of the plate

Grahic Jump Location
Fig. 2

Percentage error in Ω with varying values of n: “○”—first mode; “△”—second mode; and “□”—third mode

Grahic Jump Location
Fig. 3

Ω versus ΔT: “○”-p=0, N*=−10; “△”-p=5, N*=−10; “●”-p=0, N*=10; “▲-p=5, N*=10; clamped “-------”; simply supported “- - - - - -”

Grahic Jump Location
Fig. 4

Ω versus Kf: “○”-p=0, N*=−10; “△”-p=5, N*=−10; “●-p=0, N*=10; “▲-p=5, N*=10; clamped “------”; simply supported “- - - - - -”

Grahic Jump Location
Fig. 5

Ω versus G: “○”-p=0, N*=−10; “△”-p=5, N*=−10; “●” − p=0, N*=10; “▲”-p=5, N*=10; clamped “-------”; simply supported “- - - - - -”

Grahic Jump Location
Fig. 6

Ω versus N*: “○”-p=0, G=0; “△”-p=5, G=0; “●-p=0, G=6; “▲”-p=5, G=6; clamped “------”; simply supported “- - - - - -”

Grahic Jump Location
Fig. 7

Ω versus Ncr*: “○”-p=0, G=0; “△”-p=5, G=0; “●-p=0, G=6; “▲”-p=5, G=6; clamped “-------”; simply supported “- - - - - -”

Grahic Jump Location
Fig. 8

Ω versus ΔT: G = 0, Kf = 60, p = 5; “○”-UTD, N*=−10; “□”-LTD, N*=−10; “△”-NTD, N*=−10; “●-UTD, N*=10; “▪”-LTD, N*=10; “▲”-NTD, N*=10; clamped “-------”; simply supported “- - - - - -”

Grahic Jump Location
Fig. 9

Ω versus ΔT: Kf=0, G=2, p=5; “○”-TI, N*=−10; “△”-TD, N*=−10; “● -TI, N*= 10; “▲”-TI , N*= 10; clamped “-------”; simply supported “- - - - - -”

Grahic Jump Location
Fig. 10

First three mode shapes for p=5, Kf=60, G=6, N*=30, ΔT=400



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