Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] J. Fadle, Die Selbstspannungs-Eigenwertfunktionen der quadratischen Scheibe, Ing.-Arch. 11 (1940), 125–149 (German). MR 0002307
  • [2] P. F Papkovitsch, Über eine Form der Lösung des byharmonischen Problems für das Rechteck, C. R. (Doklady) Acad. Sci. URSS (N.S.) 27 (1940), 334–338 (German). MR 0004163
  • [3] P. F. Papkowitsch, Zwei Fragen zur Theorie der dünnen elastischen Platten, J. Appl. Math. Mech. [Akad. Nauk SSSR. Zhurnal Prikl. Mat. Mech.] 5 (1941), 359–374 (Russian, with German summary). MR 0008025
  • [4] J. L. Klemm and R. W. Little, Saint-Venant' s principle, Tech. Report No. 10, Div. of Engg. Research, Michigan State Univ. (1971)
  • [5] L. S. D. Morley, Simple series solution for the bending of a clamped rectangular plate under uniform normal load, Quart. J. Mech. Appl. Math. 16 (1963), 109–114. MR 0145739, https://doi.org/10.1093/qjmam/16.1.109
  • [6] F. A. Gaydon, The clamped, thin, rectangular plate under transverse loading, Quart. J. Mech. & Appl. Math. (1966)
  • [7] 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)
  • [8] S. Nemat-Nasser (ed.), Mechanics today. Vol. 5, Pergamon Press, Oxford-New York, 1980. Pergamon Mechanics Today Series. MR 591499
  • [9] M. S. Troitsky, Stiffened plates-bending, stability and vibrations, Elsevier, 1976

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 73K10, 73H05

Retrieve articles in all journals with MSC: 73K10, 73H05


Additional Information

DOI: https://doi.org/10.1090/qam/856181
Article copyright: © Copyright 1986 American Mathematical Society


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website