Finite Difference Simulation of a Flexible Plate Structure

Abstract

In this paper, an investigation into the dynamic characterisation of a two dimensional (2D) flexible structure is presented. A thin, flat plate, with all edges clamped, is considered. A simulation algorithm characterising the dynamic behaviour of the plate is developed through a discretisation of the governing partial differential equation formulation of the plate dynamics using finite difference methods. The algorithm is implemented within the Matlab environment, and it allows application and sensing of a disturbance signal at any mesh point on the plate. Such a provision is desirable for the design and development of active vibration control techniques for the system. The performance of the developed algorithm in characterising the dynamic behaviour of the system is assessed in comparison with previously reported results using various other methods. The validation of the algorithm is presented in both the time and frequency domains. Investigations reveal that the measured parameters associated with the first five resonance modes of the system compare favourably with previously reported results. The simulation algorithm thus developed and validated forms a suitable test and verification platform in subsequent investigations for development of active vibration control strategies for flexible plate structures.