Reconstructing Jacobi Matrices from Three Spectra

Cut a Jacobi matrix into two pieces by removing the n-th column and n-th row. We give neccessary and sufficient conditions for the spectra of the original matrix plus the spectra of the two submatrices to uniqely determine the original matrix. Our result contains Hostadt's original result as a special case

Localizing a notch in a rod from changes in node positions

This paper is an analytical/experimental investigation of the effect of damage on the nodes of free vibration modes of a thin rod in longitudinal vibration. The damage, a notch, is simulated by a simple spring. It is shown that nodes move towards the notch. The direction and amount by which they move may be used to estimate the position and severity of the damage. Analytical results agree well with experimental tests

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