0
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

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

Rahul Saini

Department of Mathematics,
IITR,
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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

Koizumi, M. , 1993, “ The Concept of FGM,” Ceram. Trans. Func. Grad. Mater., 34, pp. 3–10.
Mahamood, R. M. , Akinlabi, E. T. , and Shukla, M. P. , 2012, “ Functionally Graded Material: An Overview,” World Congress on Engineering, London, July 4--6, pp. 1–5.
Swaminathan, K. , and Sangeetha, D. M. , 2017, “ Thermal Analysis of FGM Plates—A Critical Review of Various Modeling Techniques and Solution Methods,” Compos. Struct., 160, pp. 43–60. [CrossRef]
Timoshenko, S. P. , and Gere, J. M. , 1961, Theory of Elastic Stability, 2nd ed., McGraw-Hill Book Company, New York.
Brush, D. O. , and Almorth, B. O. , 1975, Buckling of Bars, Plates and Shells, McGraw-Hill, New York.
Leissa, A. W. , 1982, “Advances and Trends in Plate Buckling Research (No. TR-2),” The Ohio State University Research Founation Columbus, Columbus, OH, Report No. 762059/712715.
Wang, C. M. , Wang, C. Y. , and Reddy, J. N. , 2004, Exact Solution for Buckling of Structural Members, CRC Press, Boca Raton, FL.
Wang, Y. H. , Tham, L. G. , and Cheung, Y. K. , 2005, “ Beams and Plates on Elastic Foundations: A Review,” Prog. Struct. Eng. Mater., 7(4), pp. 174–82. [CrossRef]
Ventsel, E. , and Krauthammer, T. , 2001, Thin Plates and Shells: Theory: Analysis, and Applications, Vol. 55, Marcel Dekker, New York.
Kohli, G. S. , and Singh, T. , 2015, “ Review of Functionally Graded Materials,” J. Prod. Eng., 18(2), pp. 1–4.
Prakash, T. , and Ganapathi, M. , 2006, “ Asymmetric Flexural Vibration and Thermoelastic Stability of FGM Circular Plates Using Finite Element Method,” Composites, Part B, 37(7–8), pp. 642–649. [CrossRef]
Jomehzadeh, E. , Saidi, A. R. , and Atashipour, S. R. , 2009, “ An Analytical Approach for Stress Analysis of Functionally Graded Annular Sector Plates,” Mater. Des., 30(9), pp. 3679–3685. [CrossRef]
Malekzadeh, P. , Haghighi, M. R. G. , and Atashi, M. M. , 2011, “ Free Vibration Analysis of Elastically Supported Functionally Graded Annular Plates Subjected to Thermal Environment,” Meccanica, 46(5), pp. 893–913. [CrossRef]
Wang, Q. , Shi, D. , Liang, Q. , and Shi, X. , 2016, “ A Unified Solution for Vibration Analysis of Functionally Graded Circular, Annular and Sector Plates With General Boundary Conditions,” Composites, Part B, 88, pp. 264–294. [CrossRef]
Jafarinezhad, M. R. , and Eslami, M. R. , 2017, “ Coupled Thermoelasticity of FGM Annular Plate Under Lateral Thermal Shock,” Compos. Struct., 168, pp. 758–771. [CrossRef]
Jabbari, M. , Shahryari, E. , Haghighat, H. , and Eslami, M. R. , 2014, “ An Analytical Solution for Steady State Three Dimensional Thermoelasticity of Functionally Graded Circular Plates Due to Axisymmetric Loads,” Eur. J. Mech. A/Solids, 47, pp. 124–142. [CrossRef]
Behravan Rad, A. , 2015, “ Thermo-Elastic Analysis of Functionally Graded Circular Plates Resting on a Gradient Hybrid Foundation,” Appl. Math. Comput., 256, pp. 276–298.
Lal, R. , and Ahlawat, N. , 2015, “ Axisymmetric Vibrations and Buckling Analysis of Functionally Graded Circular Plates Via Differential Transform Method,” Eur. J. Mech. A/Solids, 52, pp. 85–94. [CrossRef]
Farhatnia, F. , Ghanbari-Mobarakeh, M. , Rasouli-Jazi, S. , and Oveissi, S. , 2017, “ Thermal Buckling Analysis of Functionally Graded Circular Plate Resting on the Pasternak Elastic Foundation Via the Differential Transform Method,” Facta Univ. Ser. Mech. Eng., 15(3), pp. 545–563. [CrossRef]
Lyu, P. , Du, J. , Liu, Z. , and Zhang, P. , 2017, “ Free in-Plane Vibration Analysis of Elastically Restrained Annular Panels Made of Functionally Graded Material,” Compos. Struct., 178, pp. 246–259. [CrossRef]
Żur, K. K. , 2018, “ Quasi-Green's Function Approach to Free Vibration Analysis of Elastically Supported Functionally Graded Circular Plates,” Compos. Struct., 183, pp. 600–610. [CrossRef]
Żur, K. K. , 2018, “ Free Vibration Analysis of Elastically Supported Functionally Graded Annular Plates Via Quasi-Green's Function Method,” Composites, Part B, 144, pp. 37–55. [CrossRef]
Wu, T. Y. , Wang, Y. Y. , and Liu, G. R. , 2002, “ Free Vibration Analysis of Circular Plates Using Generalized Differential Quadrature Rule,” Comput. Methods Appl. Mech. Eng., 191(46), pp. 5365–5380. [CrossRef]
Reddy, J. N. , 2008, Theory and Analysis of Elastic Plates and Shells, CRC Press, London.
Paradoen, G. C. , 1977, “ Asymmetric Vibration and Stability of Circular Plates,” Comp. Struct., 9(1), pp. 89–95. [CrossRef]
Azimi, S. , 1988, “ Free Vibration of Circular Plates With Elastic Edge Supports Using the Receptance Method,” J. Sound Vib., 120(1), pp. 19–35. [CrossRef]
Gupta, U. S. , and Ansari, A. H. , 1998, “ Free Vibration of Polar Orthotropic Circular Plates of Variable Thickness With Elastically Restrained Edge,” J. Sound Vib., 213(3), pp. 429–45. [CrossRef]
Pradhan, K. K. , and Chakraverty, S. , 2015, “ Free Vibration of Functionally Graded Thin Elliptic Plates With Various Edge Supports,” Struct. Eng. Mech., 53(2), pp. 337–54. [CrossRef]
Raju, K. K. , 1986, “ A Study of Various Effects on the Stability of Circular Plates,” Comput. Struct., 24, pp. 39–45.

Figures

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

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In