Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-22T13:25:43.360Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal design of turbines with an attached mass

Published online by Cambridge University Press:  15 September 2003

Boris P. Belinskiy ,
C. Maeve McCarthy  and
Terry J. Walters
Boris P. Belinskiy
Affiliation:
Department of Mathematics, University of Tennessee at Chattanooga, 615 McCallie Avenue, Chattanooga, TN 37403-2598, USA.
C. Maeve McCarthy
Affiliation:
Department of Mathematics & Statistics, Murray State University, Faculty Hall 6C, Murray, KY 42071-3341, USA; [email protected].
Terry J. Walters
Affiliation:
Department of Mathematics, University of Tennessee at Chattanooga, 615 McCallie Avenue, Chattanooga, TN 37403-2598, USA.
Get access

Abstract

We minimize, with respect to shape, the moment of inertia of a turbine having the given lowest eigenfrequency of the torsional oscillations. The necessary conditions of optimality in conjunction with certain physical parameters admit a unique optimal design.

Keywords

Optimal designdiskmoment of inertiaSturm–Liouville problemleast eigenvaluerearrangementHelly's principleCalculus of Variations.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 9 , January 2003 , pp. 217 - 230
Copyright
© EDP Sciences, SMAI, 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

L.C. Andrews, Elementary Partial Differential Equations with Boundary Value Problems. Academic Press, Orlando, Florida (1986).
L. Collatz, Eigenwertaufgaben Mit Technischen Anwendungen. Akademische Verlagsgesellschaft, Geest $\&$ Portig K.-G., Leipzig (1963) 41-42 (in German).
Cox, S.J., The Two Phase Drum with the Deepest Base Note. Japan J. Ind. Appl. Math. 8 (1991) 345-355. CrossRef
Cox, S.J. and McCarthy, C.M., The Shape of the Tallest Column. SIAM J. Math. Anal. 29 (1998) 1-8. CrossRef
Dym, C.L., On some recent approaches to structural optimization. J. Sounds & Vibration 32 (1974) 49-70. CrossRef
Hinton, D.B., Eigenfunction expansions for a singular eigenvalue problem with eigenparameter in the boundary condition. SIAM J. Math. Anal. 12 (1981) 572-584. CrossRef
Hinton, D.B., An expansion theorem for an eigenvalue problem with eigenvalue parameter in the boundary condition. Quart. J. Math. Oxford 2 (1979) 33-42. CrossRef
Keller, J.B. and Niordson, F.I., The tallest column. J. Math. Mech. 16 (1966) 433-446.
G. Polya and G. Szego, Isoperimetric Inequalites in Mathematical Physics. Princeton University Press, Princeton, NJ, Ann. Math. Stud. 27 (1951).
D. Porter and D. Stirling, Integral Equations. Cambridge University Press, Cambridge, UK (1990).
W. Rudin, Principles of Mathematical Analysis, 3rd Ed. McGraw-Hill, New York (1976).
Taylor, J.E., Minimum mass bar for axial vibrations at specified natural frequency. AIAA J. 5 (1967) 1911-1913. CrossRef
Taylor, J.E., The strongest column: The energy approach. J. Appl. Mech. 34 (1967) 486-487. CrossRef
Taylor, J.E. and Liu, C.Y., On the optimal design of columns. AIAA J. 6 (1968) 1497-1502. CrossRef
Turner, M.J., Design of minimum mass structures with specified natural frequencies. AIAA J. 5 (1967) 406-412. CrossRef