0
TECHNICAL PAPERS

On the Optimal Shape of a Rotating Rod

[+] Author and Article Information
T. M. Atanackovic

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

J. Appl. Mech 68(6), 860-864 (Apr 15, 2001) (5 pages) doi:10.1115/1.1409938 History: Received September 26, 2000; Revised April 15, 2001
Copyright © 2001 by ASME
Your Session has timed out. Please sign back in to continue.

References

Stodola, A., 1906, Steam Turbines, D. Van Nostrand, New York.
Odeh,  F., and Tadjbakhsh,  I., 1965, “A Nonlinear Eigenvalue Problem for Rotating Rods,” Arch. Ration. Mech. Anal., 20, pp. 81–94.
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.
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.
Atanackovic,  T. M., 1987, “Stability of Rotating Compressed Rod With Imperfections,” Math. Proc. Cambridge Philos. Soc., 101, pp. 593–607.
Atanackovic,  T. M., 1997, “On the Rotating Rod With Variable Cross Section,” Archive Appl. Mechnics, 67, pp. 447–456.
Clément,  Ph., and Descloux,  J., 1991, “A Variational Approach to a Problem of Rotating Rods,” Arch. Ration. Mech. Anal., 114, pp. 1–13.
Antman, S. S., 1995, Nonlinear Problems of Elasticity, Springer, New York.
Atanackovic, T. M., 1997, Stability Theory of Elastic Rods, World Scientific, Singapore.
Atanackovic,  T. M., and Simic,  S. S., 1999, “On the Optimal Shape of a Pflüger Column,” Eur. J. Mech. A/Solids, 18, pp. 903–913.
Clausen,  T., 1851, “Über die Form architektonischer Säulen,” Bull. cl, physico math. Acad. St. Pétersbourg, 9, pp. 369–380.
Blasius,  H., 1914, “Träger kleinster Durchbiegung und Stäbe großter Knickfestigkeit bei gegebenem Materialverbrauch,” Zeitsch. Math. Physik, 62, pp. 182–197.
Ratzersdorfer, J., 1936, Die Knickfestigkeit von Stäben und Stabwerken, Springer, Wien.
Keller,  J., 1960, “The Shape of the Strongest Column,” Arch. Ration. Mech. Anal., 5, pp. 275–285.
Cox,  S. J., 1992, “The Shape of the ideal Column,” The Mathematical Intelligencer, 14, pp. 16–24.
Chow, S.-N., and Hale, J. K., 1982, Methods of Bifurcation Theory, Springer, New York.
Keller,  J. B., and Niordson,  F. I., 1966, “The Tallest Column,” J. Math. Mech., 16, pp. 433–446.
Cox,  S. J., and McCarthy,  C. M., 1998, “The Shape of the Tallest Column,” SIAM (Soc. Ind. Appl. Math.) J. Math. Anal., 29, pp. 547–554.
Sage, A. P., and White, C. C., 1977, Optimum System Control, Prentice-Hall, Englewood Cliffs, NJ.
Alekseev, V. M., Tihomirov, V. M., and Fomin, S. V., 1979, Optimal Control, Nauka, Moscow (in Russian).
Pierson,  B. L., 1977, “An Optimal Control Approach to Minimum-Weight Vibrating Beam Design,” J. Structural Mechanics, 5, pp. 147–178.
Carmichael,  D., 1977, “Singular Optimal Control Problems in the Design of Vibrating Structures,” J. Sound Vib., 53, pp. 245–253.
Carmichael, D., 1981, Structural Modelling and Optimization: A General Methodology for Engineering and Control, Ellis Horwood, Chichester, UK.

Figures

Grahic Jump Location
The optimal cross-sectional area
Grahic Jump Location
Optimal rod and rod with constant cross section

Tables

Errata

Discussions

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