Optimum design of vibrating cantilevers

  • B. L. Karihaloo
  • F. I. Niordson


We determine the optimum tapering of a cantilever carrying an end mass, i.e., the shape which, for a given total mass, yields the highest possible value of the first fundamental frequency of harmonic bending vibrations in the vertical plane.

Three different cases are considered. In the first case, all cross sections are assumed to be geometrically similar. In the second case, the cross sections are assumed to be rectangular and of given width. Finally, we consider a rectangular cross section of given height. This third case is shown to be degenerate in the absence of end mass.


Fundamental Frequency Cantilever Beam Optimum Shape Rectangular Cross Section Propol 
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  1. 1.
    Niordson, F. I.,On the Optimal Design of a Vibrating Beam, Quarterly of Applied Mathematics, Vol. 23, No. 1, 1965.Google Scholar
  2. 2.
    Olhoff, N.,Optimal Design of Vibrating Circular Plates, International Journal of Solids and Structures, Vol. 6, No. 1, 1970.Google Scholar
  3. 3.
    Timoshenko, S. P.,Vibration Problems in Engineering, D. Van Nostrand Company, New York, 1966.Google Scholar
  4. 4.
    Collatz, L.,Eigenwertaufgaben mit Technischen Anwendungen, Akademische Verlagsgesellschaft Geest & Portig K.-G., Leipzig, Germany, 1963.Google Scholar
  5. 5.
    Brach, R. M.,On the Extremal Fundamental Frequencies of Vibrating Beams, International Journal of Solids and Structures, Vol. 4, No. 6, 1968.Google Scholar

Copyright information

© Plenum Publishing Corporation 1973

Authors and Affiliations

  • B. L. Karihaloo
    • 1
  • F. I. Niordson
    • 1
  1. 1.Department of Solid MechanicsThe Technical University of DenmarkLyngbyDenmark

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