Identification of Beam Boundary Conditions Using Displacement Derivatives Estimations

The purpose of the study is to illustrate the possibility of boundary conditions identification in case of beams. The problem is understood as a determination of various spatial derivatives of transverse displacements. Using the assumption that displacements can be approximated by Taylor expansions on a domain near its boundaries, the spatial derivatives are estimated using particular pointwise derivatives estimators. This approach enables the extraction of these quantities using a weighted spatial integration of the displacement field. Numerical simulation using exact and noisy data are shown in order to clarify the link between the size of the integration domain and the wavelengths of the vibrations.