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.
