Numerical modelling of a flexible plate system

Abstract

The dynamic behaviour of thin isotropic rectangular plates is a subject that has received considerable attention in recent years because of its technical importance. In addition to being a problem of academic interest many applications of thin flat plates are found in industry. Examples are found in bridge decks, solar panels, and electronic circuit board design. The control of a vibrating plate is, however, complicated due to the highly non-linear dynamic nature of the system, which involves complex processes. It is important initially to recognize the flexible nature of the plate and construct a mathematical model for the system. In order to control the vibration of a plate efficiently, it is required to obtain an accurate model of the plate structure. An accurate model will result in satisfactory and good control. Such a model can be constructed using a partial differential equations (PDE) formulation of the dynamics of the flexible plate. A commonly used approach for solving the PDE, representing the dynamics of the plate, is to utilize a representation of the PDE, obtained through a simplification process, by a finite set of ordinary differential equations.