Exact construction of beams with a finite number of given natural frequencies

In this paper an analytical, exact procedure for the reconstruction of simply supported bending vibrating beams having given values of the first N natural frequencies is presented. The results hold for beams in which the product between the bending stiffness and the linear mass density is constant. The analysis is based on the fact that this class of beams is spectrally equivalent to a family of strings fixed at the ends, and uses recent results on the exact construction of second-order Sturm-Liouville operators with prescribed natural frequencies. The analysis can be adapted to beams with pinned-sliding and sliding-sliding ends.