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Uniqueness in the identification of asynchronous sources and damage in vibrating beams

In this paper we analyze the problem of identification of the distribution of asynchronous vibration sources and rigidity perturbations in Euler-Bernoulli beams. Here it is proved that the displacement of a beam, even in an engineered continuous beam resting upon several supports, measured for an arbitrary small interval of time over an arbitrary small open set is enough for the unique determination of vibration sources. Using this result, we prove that perturbations in rigidity can be uniquely determined in a linearized problem.