Identifiability of distributed parameters in beam-type systems (Q2712499)

The coefficient identifiability problem for the Euler-Bernoulli theory for beam-type systems is considered. For a fourth-order with respect to the space variable and second-order with respect to the time variable partial differential equation, the author studies the identification of coefficients, which correspond to the flexural rigidity and the mass per unit length of the beam. The deflection and load subjected to the beam are given and belong to an admissible set of functions. The unknown coefficients representing physical properties of the beam are looked for in the set of strictly positive and sufficiently differentiable functions. In this setup the identifiability is equivalent to the uniqueness of the solution of the inverse problem. Necessary and sufficient conditions are established for the identifiability or non-identifiability of the unknown coefficients. Results are demonstrated by examples.