Abstract
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.
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References
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Communicated by W. Prager
The first author takes the opportunity of thanking the authorities of the Technical University of Denmark for generous financial aid for his work at the University. We also thank our colleague Lic. Techn. Niels Olhoff for many valuable discussions during the course of the numerical computations.
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Karihaloo, B.L., Niordson, F.I. Optimum design of vibrating cantilevers. J Optim Theory Appl 11, 638–654 (1973). https://doi.org/10.1007/BF00935563
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DOI: https://doi.org/10.1007/BF00935563