Identification of the flexural stiffness parameters of an orthotropic plate from the local dynamic equilibrium without a priori knowledge of the principal directions

This paper proposes an inverse method to characterize orthotropic material properties from vibratory measurements on plate-like structures. The method is an adaptation of the Force Analysis Technique (FAT), which was originally developed to identify the external force distribution acting on a structure using its local discretized equation of motion. This method was recently adapted to the identification of elastic and damping properties of isotropic plates. In the present approach, the equation of motion of an orthotropic plate with respect to an arbitrary set of orthogonal axes is considered. The angle between the axes of the measurement mesh and the principal directions of orthotropy therefore explicitly appears in the equation and constitutes an unknown. A procedure to identify this angle together with the flexural stiffness parameters is proposed, as well as an automatic regularization procedure to overcome the high sensitivity of the inverse problem to measurement noise. The method is illustrated using simulated data. Experimental results shown on various structures demonstrate the ability of the method to simultaneously identify the principal orthotropy directions and the flexural stiffness parameters.