On a class of eigenvalue problems of orthotropic plates
Authors:
Chiruvai P. Vendhan and Subroto Kumar Bhattacharyya
Journal:
Quart. Appl. Math. 44 (1986), 277-292
MSC:
Primary 73K10; Secondary 73H05
DOI:
https://doi.org/10.1090/qam/856181
MathSciNet review:
856181
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Abstract: A class of eigenvalue problems for linear bending of semi-infinite orthotropic plates under the action of in-plane stress resultant in the finite direction has been developed. The structure of the eigenvalues has been investigated analytically for the case of simply supported plates and their physical basis underscored. It is shown that the treatment results in a coupled eigenvalue problem of bending as well as bifurcation buckling, thereby suggesting an alternate criterion for buckling.
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F. A. Gaydon, The clamped, thin, rectangular plate under transverse loading, Quart. J. Mech. & Appl. Math. (1966)
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J. Fadle, Die Selbstspannungs-Eigenwert funktionen der quadratischen Scheibe, Ingen. Archiv. 11, 125–149 (1940)
P. F. Papkovitsch, Über eine Form der Lösung des byharmonischen Problems für das Rechteck, C. R. Doklady, Academy of Science, URSS (N.S.) 27, 334–338 (1940)
P. F. Papkovitsch, Zwei Fragen zur Theorie der dünnen elastischen Platten, J. Appl. Math. Mech. [Akad. Nauk SSSR. Zhurnal Prikl. Mat. Mech.] 5, 359–374 (1941)
J. L. Klemm and R. W. Little, Saint-Venant’ s principle, Tech. Report No. 10, Div. of Engg. Research, Michigan State Univ. (1971)
L. S. D. Morley, Simple series solution for the bending of a clamped rectangular plate under uniform normal load, Quart. J. Mech. & Appl. Math. (1963)
F. A. Gaydon, The clamped, thin, rectangular plate under transverse loading, Quart. J. Mech. & Appl. Math. (1966)
B. S. Ramachandra Rao, G. L. Narasimham and S. Gopalacharyulu, Eigenfunction analysis for bending of clamped, rectangular, orthotropic plates, Int. J. Solids and Structures (1973)
R. R. Archer and N. Bandopadhyay, On the ’end problem’ for thick rectangular plates, Mechanics Today, vol. 5, Ed. by S. Nemat-Nasser, pp. 1–13, Pergamon, Oxford, (1978)
M. S. Troitsky, Stiffened plates-bending, stability and vibrations, Elsevier, 1976
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Article copyright:
© Copyright 1986
American Mathematical Society
