Determining expressions for the strain and kinetic energies and the external work, taking their variations and substituting into Hamilton's Principle.
A detailed derivation of the kinetic energy of a beam can be found in this video:
youtube.com/watch?v=8GV5pggBeu0
Download notes for THIS video HERE: [ Ссылка ]
Download notes for my other videos: [ Ссылка ]
Reference: Dym & Shames, Solid Mechanics: A Variational Approach
[ Ссылка ]
CHAPTERS:
0:00 Continuing
0:25 Getting Started
1:03 Displacement Field
4:09 Strains
7:28 Stresses
11:57 Strain Energy
19:17 Variation of the Strain Energy
24:35 Kinetic Energy
31:13 Variation of the Kinetic Energy
31:48 External Work
32:11 Variation of External Work
