Optimum design of vibrating cantilevers: A classical problem revisited (Q1893333)

The problem, originally formulated and solved by \textit{B. L. Karihaloo} and \textit{F. I. Niordson} [ibid. 11, 638-654 (1973; Zbl 0256.73021)] was to find the optimal beam shape that will maximize the fundamental vibration frequency of a cantilever. Upon reexamination of the problem, it has been found that the original analysis and solution procedure can be simplified and improved substantially. Specifically, we give a new set of simplified equations for the construction of iteration schemes. New asymptotic expressions for the optimum design solution have been obtained and verified by numerical results. Also some obvious numerical errors in the original paper have been identified and corrected.