Localisation and identification of sources on laminated structures: extension of CFAT method

In the literature, several papers deal with the localisation and quantification of forces on a structure. One of them, the FAT (Force Analysis Technique) method, which was recently extended to material characterisation, was initially created for vibration source identification. This method was developed for beams, isotropic plates or shells and recently orthotropic plates. FAT identifies the equation of motion of the structure with a finite difference scheme applied on a measured displacement field. This scheme gives an approximation of the partial derivatives. By introducing correction factors, the CFAT (Corrected FAT) methodology corrects the approximation made by finite difference scheme and attenuates the singularities of the filter. This paper presents the extension of this last method for laminated plates. This type of plate is different from an orthotopic plate because it presents a flexural-torsion interaction and has a complex equation of motion with 5 flexural rigidities (against 3 in the orthotropic case and 1 in the isotropic case). The correction of the finite difference scheme is now composed of 5 correction factors estimated in this paper analytically and numerically. Finally, a validation of the extension of CFAT is presented on numerical displacement field (FEM Nastran) for laminated plates.