Modelling of high-order mechanical plate vibration systems by multidimensional wave digital filters

The application of the MDWDF technique, derived from the wave digital filter (WDF) paradigm, to the modelling of a Mindlin plate vibration system is presented. Initial and boundary conditions of the plate vibration system are properly embedded in the MDWDF algorithm in terms of state output quantities, which are fully implemented in the algorithm. More specifically, different types of boundary conditions encountered in practice can be easily fulfilled in a very simple and efficient manner without remodifying the whole algorithm, which is usually proceeded by a finite elements based method with various boundary conditions. This is due to the local connectivity of the MDWDF model, in the sense that the behaviour at any point on the grid is directly influenced only by its nearest-neighbour grid points. Graphical results illustrating the plane wave propagation on a square plate are given for which free edges boundary conditions are fully considered.