Identification of an unknown spatial load distribution in a vibrating beam or plate from the final state

The theoretical and numerical determination of a space-dependent load distribution in a simply supported non-homogeneous Euler-Bernoulli beam and Kirchhoff-Love plate is investigated. The uniqueness of a solution to this inverse source problem is proved, whilst counter examples are constructed to discuss the conditions under which uniqueness holds. A convergent and stable iterative algorithm is proposed for the recovery of the unknown load source and a stopping criterion is also given. Several one-dimensional numerical experiments are considered to investigate the properties of the proposed iterative procedure.