A family of isospectral Euler-Bernoulli beams

In this paper we consider the class of Euler-Bernoulli beams such that the product between the bending stiffness and the linear mass density is constant. Under the assumption that the end conditions are any combination of pinned and sliding, we obtain closed form expressions for beams isospectral to a given one. The analysis is based on the fact that this special class of beams is, in a certain sense, equivalent to a string, and uses a Darboux lemma after reduction of the string equation to Sturm-Liouville canonical form.