Load identification in a plate-beam lattice from interior dynamic data

Abstract

We consider the inverse problem of determining transverse dynamic loads acting on a clamped plate stiffened by two sets of orthogonal beams. Under the assumption of infinitesimal deformation, in the sense that linear elasticity applies, homogeneous isotropic material and negligible beam torsional stiffness, we show that the measurement of the transverse response of the system in an open subset of the mid-plane, and for an arbitrarily small interval of time, is sufficient for the unique determination of the spatial component of the load. The uniqueness result holds for multiple asynchronous loads and suggests a reconstruction procedure, which is used for a numerical validation of the method.