A group-theoretic finite-difference formulation for plate eigenvalue problems

We consider the problem of the free vibration of plates, and develop an efficient group-theoretic formulation for the solution of the problem by the method of finite differences. The procedure requires the writing down of the finite-difference equations for a relatively small number of nodes. These equations are then transformed into uncoupled sets of symmetry-adapted equations for the various subspaces, which are solved independently to generate the eigenvalues in the original space of the problem. Not only does the procedure reduce computational effort, but it also allows valuable insights to be gained on the vibration properties of the system.

► Presents a group-theoretic formulation of the numerical method of finite differences.
► Applies the group-theoretic formulation to the eigenvalue analysis of symmetric plates.
► Illustrates the procedure by reference to the vibration of rectangular and square plates.
► Demonstrates the computational efficiency of the group-theoretic formulation.
► Provides valuable insights into the vibration behaviour of symmetric plates.