Understanding and Applying Structural Dynamics

This course sums up the foundation of solid dynamics applied to structural analysis, as follows:

• A first item deals with the fundamental signification of dynamics. Dynamics is not simply an extension of statics, but another modeling with open possibilities (including statics, obviously). The basic theorems (Newton’s equivalence principle, König’s theorems, conservations) are detailed in the perspective of structural applications.
• The second point presents the generation of discrete dynamic systems, in the general formalism of Lagrange, well adapted for numerical modeling of dynamics. This toll is essential for the general representation of dynamic systems.
• Then the third step consists in the generation and solution of matrix equations in the frame of conservative structural systems, with Gaussian modes. This part is important for the comprehension of the eigenshapes in vibration and shocks.
• In the frame of the theory of prismatic beams, the application of the general dynamic formalism to continuous thin elementary is an example of generalization of the eigenshape theory and general dynamic representation of structures.
• The four parts can be studied sequentially or independently ; and even inside each part, elementary learning items can be picked up.