  This paper studies the inverse problem related to the identification of the
flexural stiffness of an Euler Bernoulli beam in order to reconstruct its
profile starting from available response data. The proposed identification
procedure makes use of energy measurements and is based on the application of a
closed form solution for the static displacements of multi-stepped beams. This
solution allows to easily calculate the energy related to beams modeled with
arbitrary multi-step shapes subjected to a transversal roving force, and to
compare it with the correspondent data obtained through direct measurements on
real beams. The optimal solution which minimizes the difference between
measured and calculated data is then sought by means of genetic algorithms. In
the paper several different stepped beams are investigated showing that the
proposed procedure allows in many cases to identify the exact beam profile.
However it is shown that in some other cases different multi-step profiles may
correspond to very similar static responses, and therefore to comparable minima
in the optimization problem, thus complicating the profile identification
problem.
