Quasi-isospectral Sturm-Liouville operators and applications to system identification

Quasi-isospectral Sturm-Liouville operators play an important role in inverse spectral theory and are typically used for determining exact solutions to suitable classes of eigenvalue problems with variable coefficients. In this work we investigate on alternative applications of quasi-isospectral operators as key tool for structural identification purposes. We review some recent results concerned with the construction of rods with a given finite number of natural frequencies and we present some generalization to beams under bending vibration and to the identification of damages from natural frequency data.