Source identification by Vibratory Holography

The knowledge of adverse effects caused by vibration sources is a key issues in the design and monitoring of many structures. This need has resulted in the development of many methods for locating or identifying the sources. The vibratory holography imaging technique presented here fits into this topic. %48 The method introduced in this paper is developed as classical Near-field Acoustic Holography (NAH) but in the vibratory domain. In that case, the plate displacement is measured on a one-dimensional line (the hologram) and used to reconstruct an entire two-dimensional displacement field. As in acoustic holography, the back-propagation is performed in the k-space by a Spatial Fourier Transform. However, this approach, called "Vibratory Holography", has a major difference with the acoustic holography: the order of the spatial derivatives of the equation of motion of the plate. Indeed, the fourth spatial derivatives imply an important influence of evanescent waves and require particular attention. The approach is particularly interesting when a direct measurement of the velocity field is not possible. Moreover, this method decreases the number of measurements required to reconstruct the displacement field of the entire plate. The purpose of this paper is to introduce the Vibratory Holography method. The first part presents the theoretical background of the method and the study of its parameters. The second part presents some results of propagation and back-propagation for a numerical simulation. The influence of some simulation parameters is studied. Finally the method is used on a simply supported plate.