Abstract
It is known that the cross-sectional profile of a longitudinally vibrating, straight, slender rod may be constructed uniquely, apart from a scale factor, from two spectra of natural frequencies corresponding to two different end conditions at one end of the rod. In this paper examples of the Gel'fand-Levitan construction of such a rod are presented. Numerical results are presented for the slenderness ratio of such a rod as functions of the prescribed data, and for the actual cross-sectional profiles of typical rods.
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