Uniqueness in the determination of unknown coefficients of an Euler-Bernoulli beam equation with observation in an arbitrary small interval of time

In the present article, we prove an uniqueness result for the non-linear problem of identifying the flexural stiffness and density of an Euler-Bernoulli beam using observation of boundary measurements. Here we show that the knowledge of the displacement and slope of at the free extremity of a clamped-free vibrating beam, for an arbitrary small interval of time, leads to the uniqueness in the identification of its rigidity and density. This result extends previous works that showed that the identification was possible when the observation was collected in an unbounded interval of time, or when the original dynamic problem for the Euler-Bernoulli beam was linearised.