On the Optimal Shape of a Rotating Rod-Reference-Cited by-同舟云学术

On the Optimal Shape of a Rotating Rod

Published:2001-04-15 Issue:6 Volume:68 Page:860-864
ISSN:0021-8936
Container-title:Journal of Applied Mechanics
language:en
Short-container-title:

Author:

Atanackovic T. M.¹

Affiliation:

1. Faculty of Technical Sciences, University of Novi Sad, 21000 Novi Sad, Yugoslavia

Abstract

By using Pontryagin’s maximum principle we determine the shape of the lightest rotating rod, stable against buckling. It is shown that the cross-sectional area function is determined from the solution of a nonlinear boundary value problem. Three variational principles for this boundary value problem are formulated and a first integral is constructed. The optimal shape of a rod is determined by numerical integration.

Publisher

ASME International

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Link

http://asmedigitalcollection.asme.org/appliedmechanics/article-pdf/68/6/860/5468494/860_1.pdf

Reference23 articles.

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2. Odeh, F., and Tadjbakhsh, I., 1965, “A Nonlinear Eigenvalue Problem for Rotating Rods,” Arch. Ration. Mech. Anal., 20, pp. 81–94.

3. Bazely, N., and Zwahlen, B., 1968, “Remarks on the Bifurcation of Solutions of a Non-linear Eigenvalue problem,” Arch. Ration. Mech. Anal., 28, pp. 51–58.

4. Parter, S. V. , 1970, “Nonlinear Eigenvalue Problems for Some Fourth Order Equations: I—Maximal Solutions,” SIAM (Soc. Ind. Appl. Math.) J. Math. Anal., 1, pp. 437–457, and “II—Fixed-Point Methods,” 1, pp. 458–478.

5. Atanackovic, T. M. , 1987, “Stability of Rotating Compressed Rod With Imperfections,” Math. Proc. Cambridge Philos. Soc., 101, pp. 593–607.

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