The problem of a cantilever beam was explored in class during Session #19. The following materials give more details about the analysis and the 6 modes corresponding to the lowest 6 frequencies. If images/text are blurry, please zoom in.
Dynamic analysis of a cantilever beam (PDF)
Mode 1 (AVI)
Mode 2 (AVI)
Mode 3 (AVI)
Mode 4 (AVI)
Mode 5 (AVI)
Mode 6 (AVI)
The natural frequencies of a cube were investigated using ADINA, and the results checked against theory. (PDF)
Finite Element Procedures for Solids and Structures presents two video courses by Prof. Bathe, recommended for further study on the topics of linear and nonlinear finite element analysis.