Analytical study uncovers closed-form isospectral Euler–Bernoulli beams with constant stiffness-density products, indicating string equivalence via Darboux transformations.
In this paper we consider the class of Euler-Bernoulli beams such the product between the bending stiffness and the linear mass is constant. Under the assumption that the end conditions any combination of pinned and sliding, we obtain closed form for beams isospectral to a given one. The analysis is on the fact that this special class of beams is, in a sense, equivalent to a string, and uses a Darboux lemma reduction of the string equation to Sturm-Liouville form.
No takes yet. Share an insight, caveat, or question.
Gladwell et al. (2010) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: