Identification of variable spacial coefficients for a beam equation from boundary measurements

We consider a system described by the Euler–Bernoulli beam equation, with one end clamped and with torque input at the other end. The output function are the displacement and the angle velocity at the non-clamped end of the beam. We study the identification of the spatially variable coefficients in the beam equation, from input–output data. We show that both the density and the flexural rigidity of the beam (which are assumed to be of class C4C4) can be uniquely determined if the input and output functions are known for all positive times.