Ricerc@Sapienza

Modal curvatures have been claimed to contain local information on damage and to be less sensitive to environmental variables than natural frequencies. However, simply using the difference between modal curvatures in the undamaged and damaged states can result into localization errors, due to the complex pattern that this quantity presents when considering broad damages or higher order modes.

We investigate the simultaneous observability of infinite systems of vibrating strings or beams having a common endpoint where the observation is taking place. Our results are new even for finite systems because we allow the vibrations to take place in independent directions. Our main tool is a vectorial generalization of some classical theorems of Ingham, Beurling and Kahane in nonharmonic analysis.