Vibration Analysis Of Kirchhoff Plates By The Nonconforming Element Method With Mass-Lumping

Plates are the basic components in elastic structures. Their vibration analysis is of great importance in many applied fields, such as civil, mechanical, aerospace engineering, etc. The semi-discrete Morley element method for the problem and its error estimates in the energy norm are reviewed first. Then, using the second-order central difference to discretize the time derivative of the displacement, and applying the quadrature formula to the mass matrix, a fully discrete lumped mass Morley element method is developed for the same problem. Since the technique of mass-lumping is borrowed, the resulting linear system is easy to solve comparatively. The convergence rate in the energy norm is established in terms of error estimates for the quadrature formula involved combined with error estimates for the static problem. A series of numerical results are given to illustrate the effectiveness and efficiency of the method being proposed in this thesis.