Low order modeling of a metal plate under vibrations

The Proper Orthogonal Decomposition (POD) method and the Galerkin projection are applied to study vibrations on an aluminum square plate. Data from the plate vibrations were obtained using a Laser Vibrometer and the Fringe Projection technique. The vibrations, within the range 100 to 5,000 Hz, on the metal plate were produced with an electrodynamical shaker. Due to the symmetrical nature of the plate, the vertical displacement velocity measurements were taken only on a rectangular grid of 7X8 points. The vertical displacement velocity measured at different locations and times, was synchronized with a full-field instantaneous image of the plate obtained from the Fringe Projection technique. The plate vibration measurements were used to calculate its eigenfunctions and the eigenvalues. It was found that a large fraction of the total energy of the vibration is contained within the first two POD modes. The essential features of the vibration are thus described by only the first two eigenfunctions. A reduced order model for the dynamical behavior is then constructed using the Galerkin projection of the equation of motion for the vertical displacement of a plate.