Optimal design of turbines with an attached mass
ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 217-230

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.

DOI : 10.1051/cocv:2003011
Classification : 49K15, 49K30, 34B24, 49R05, 73K10, 73K40
Keywords: optimal design, disk, moment of inertia, Sturm-Liouville problem, least eigenvalue, rearrangement, Helly's principle, calculus of variations 
@article{COCV_2003__9__217_0,
     author = {Belinskiy, Boris P. and McCarthy, C. Maeve and Walters, Terry J.},
     title = {Optimal design of turbines with an attached mass},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {217--230},
     year = {2003},
     publisher = {EDP Sciences},
     volume = {9},
     doi = {10.1051/cocv:2003011},
     mrnumber = {1957100},
     zbl = {1066.49025},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/cocv:2003011/}
}
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Belinskiy, Boris P.; McCarthy, C. Maeve; Walters, Terry J. Optimal design of turbines with an attached mass. ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 217-230. doi: 10.1051/cocv:2003011

[1] L.C. Andrews, Elementary Partial Differential Equations with Boundary Value Problems. Academic Press, Orlando, Florida (1986).

[2] L. Collatz, Eigenwertaufgaben Mit Technischen Anwendungen1963) 41-42 (in German). | Zbl | MR

[3] S.J. Cox, The Two Phase Drum with the Deepest Base Note. Japan J. Ind. Appl. Math. 8 (1991) 345-355. | Zbl | MR

[4] S.J. Cox and C.M. Mccarthy, The Shape of the Tallest Column. SIAM J. Math. Anal. 29 (1998) 1-8. | Zbl | MR

[5] C.L. Dym, On some recent approaches to structural optimization. J. Sounds & Vibration 32 (1974) 49-70. | Zbl

[6] D.B. Hinton, Eigenfunction expansions for a singular eigenvalue problem with eigenparameter in the boundary condition. SIAM J. Math. Anal. 12 (1981) 572-584. | Zbl | MR

[7] D.B. Hinton, An expansion theorem for an eigenvalue problem with eigenvalue parameter in the boundary condition. Quart. J. Math. Oxford 2 (1979) 33-42. | Zbl | MR

[8] J.B. Keller and F.I. Niordson, The tallest column. J. Math. Mech. 16 (1966) 433-446. | Zbl | MR

[9] G. Polya and G. Szego, Isoperimetric Inequalites in Mathematical Physics. Princeton University Press, Princeton, NJ, Ann. Math. Stud. 27 (1951). | Zbl | MR

[10] D. Porter and D. Stirling, Integral Equations. Cambridge University Press, Cambridge, UK (1990). | Zbl | MR

[11] W. Rudin, Principles of Mathematical Analysis, 3rd Ed. McGraw-Hill, New York (1976). | Zbl | MR

[12] J.E. Taylor, Minimum mass bar for axial vibrations at specified natural frequency. AIAA J. 5 (1967) 1911-1913.

[13] J.E. Taylor, The strongest column: The energy approach. J. Appl. Mech. 34 (1967) 486-487.

[14] J.E. Taylor and C.Y. Liu, On the optimal design of columns. AIAA J. 6 (1968) 1497-1502. | Zbl

[15] M.J. Turner, Design of minimum mass structures with specified natural frequencies. AIAA J. 5 (1967) 406-412. | Zbl

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