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

摘要

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.