Free access
Issue
ESAIM: COCV
Volume 9, March 2003
Page(s) 217 - 230
DOI http://dx.doi.org/10.1051/cocv:2003011
Published online 15 September 2003
  1. L.C. Andrews, Elementary Partial Differential Equations with Boundary Value Problems. Academic Press, Orlando, Florida (1986).
  2. L. Collatz, Eigenwertaufgaben Mit Technischen Anwendungen. Akademische Verlagsgesellschaft, Geest Formula Portig K.-G., Leipzig (1963) 41-42 (in German).
  3. S.J. Cox, The Two Phase Drum with the Deepest Base Note. Japan J. Ind. Appl. Math. 8 (1991) 345-355. [CrossRef]
  4. S.J. Cox and C.M. McCarthy, The Shape of the Tallest Column. SIAM J. Math. Anal. 29 (1998) 1-8. [CrossRef] [MathSciNet]
  5. C.L. Dym, On some recent approaches to structural optimization. J. Sounds & Vibration 32 (1974) 49-70. [CrossRef]
  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. [CrossRef] [MathSciNet]
  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. [CrossRef]
  8. J.B. Keller and F.I. Niordson, The tallest column. J. Math. Mech. 16 (1966) 433-446. [MathSciNet]
  9. G. Polya and G. Szego, Isoperimetric Inequalites in Mathematical Physics. Princeton University Press, Princeton, NJ, Ann. Math. Stud. 27 (1951).
  10. D. Porter and D. Stirling, Integral Equations. Cambridge University Press, Cambridge, UK (1990).
  11. W. Rudin, Principles of Mathematical Analysis, 3rd Ed. McGraw-Hill, New York (1976).
  12. J.E. Taylor, Minimum mass bar for axial vibrations at specified natural frequency. AIAA J. 5 (1967) 1911-1913. [CrossRef]
  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. [CrossRef]
  15. M.J. Turner, Design of minimum mass structures with specified natural frequencies. AIAA J. 5 (1967) 406-412. [CrossRef]