ISSN:
1573-2878
Keywords:
Cantilever beams
;
flexible manipulators
;
optimum design
;
fundamental frequency
;
successive iterations
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Optimum design of vibrating cantilevers is a classical problem widely used in the literature and textbooks in structural optimization. The problem, originally formulated and solved by Karihalloo and Niordson (Ref. 5), 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, the time-consuming inner loop devised for solving the Lagrange multiplier in the original work has been proved to be tolally unnecessary and thus should not be considered in the problem solution. This conclusion has led to 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. Numerical analysis has shown a significant improvement in convergence rate by the proposed new procedure. Also some obvious numerical errors in the original paper have been identified and corrected.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02191989
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