Alberto Torin

The basic equations describing the transverse linear vibration of thin plates using the Kirchhoff model are discussed for rectangular and circular geometries, and particular attention is devoted to the link between energy and boundary conditions in the continuous case. Then, a brief introduction on the finite difference method is presented, together with the notation adopted throughout this work. Finite difference schemes for rectangular and circular plates are presented. A complete discussion of energy-based stability techniques including the derivation of boundary conditions is provided, together with simulation results demonstrating the stability of the numerical implementations.