Identification of Plate Boundary Forces From Measured Displacements

This work deals with the identification of forces at plate boundaries, by measuring displacements only. Shear force and bending moment directly depend on different spatial derivatives of displacement at plate boundaries that can be approximated from measured displacements (finite differences, modal approach, etc.), but two major difficulties occur: Derivatives are highly sensitive to measurement errors and the usual methods used to obtain them are not well adapted to boundary points. In this paper, a mathematical approach is proposed to identify shear force at boundaries without any direct calculation of the displacement derivatives. The method is based on the weak form of the plate equation of motion and a test function satisfying particular boundary conditions. Following the description of the technique and the definition of the test function that permits the identification at one boundary point, numerical simulation results, including the effects of noise on displacements, are provided in order to establish the spatial and frequency limits of this method.