Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, November 26, 2002, final revision, May 10, 2004. Associate Editor: N. Triantafyllidis.

The stability problem of plates has been of considerable importance in engineering. For the case of a thin circular plate described by the von Ka´rma´n nonlinear plate theory stability, analysis is given by Wolkowisky 1. The stability of a clamped annular plate also described by the von Ka´rma´n nonlinear plate theory is presented by Machinek and Troger 2, where the Liapunov-Schmidt method is used. For the case of a moderately thick circular plate stability, analysis is given by Raju and Rao 3.

Many papers investigated the influence of temperature on the stability and the stress distribution of the plate....

1.
Wolkowisky
,
J. H.
,
1967
, “
Existence of Buckled States of Circular Plates
,”
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546
560
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2.
Machinek
,
A. K.
, and
Troger
,
H.
,
1988
, “
Postbuckling of Elastic Annular Plates at Multiple Eigenvalues
,”
Dyn. Stab. Syst.
,
3
, pp.
78
98
.
3.
Raju
,
K. K.
, and
Rao
,
G. V.
,
1983
, “
Postbuckling Analysis of Moderately Thick Elastic Circular Plates
,”
ASME J. Appl. Mech.
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50
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468
470
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4.
Pal
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M. C.
,
1969
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Large Deformations of Heated Circular Plates
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8
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5.
Ghosh
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N. C.
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1975
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Thermal Effect on the Transverse Vibration of Spining Disk of Variable Thickness
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42
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358
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6.
Renshaw
,
A. A.
,
1998
, “
Critical Speed for Floppy Disks
,”
ASME J. Appl. Mech.
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65
, pp.
116
120
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7.
Timoshenko, S., and Woinowsky-Krieger, S., 1959, Theory of Plates of Shells, 2nd ed. McGraw-Hill, New York.
8.
Nowacki, W., 1962, Thermoelasticity, International Series of Monograph on Aeronautics and Astronautics, 3, Addison-Wesley, Reading, MA.
9.
Abramowitz, M., and Stegun, I., 1965, Handbook of Mathematical Functions, Dover, New York.
10.
Golubitsky, M., and Schaeffer, D. G., 1985, Singularities and Groups in Bifurcation Theory, Vol. 1, Springer, New York.
11.
Chow, S. N., and Hale, J. K., 1982, Methods of Bifurcation Theory, Springer, New York.
12.
Troger, H., and Steindl, A., 1991, Nonlinear Stability and Bifurcation Theory: An Introduction for Engineers and Applied Scientisty, Springer, Wien.
13.
Keyfitz
,
B. L.
,
1986
, “
Classification of one-state variable bifurcation problems up to codimension seven
,”
Dyn. Stab. Syst.
,
1
, pp.
1
41
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14.
Maretic
,
R.
,
1998
, “
Vibration and Stability of Rotating Plates with Elastic Edge Supports
,”
J. Sound Vib.
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210
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291
294
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