Developments of structural dynamics

WEEK 1: Analytical dynamics
We will discover the power of Lagrange formalism able to generate the equation of any discrete dynamic system. This seems miraculous because, from energies, we directly extract the complete dynamic equations.

WEEK 2: Linear structures
Linearity is an important domain. Not only because it corresponds to powerfull mathematic tools but also because it's a nominal way to move for a structure. In this topic, we master the modeling of any digital linear system.

WEEK 3: Discrete eigenshapes
We solve the digital dynamic system by Gaussian diagonalization, thus we discover the concept of natural shapes (or eigenshapes), fundamental for the dynamic behavior of any structure. This opens the world towards resonances and implicit analysis. In fact, the modes represent the actual dynamic DNA of the structure.

WEEK 4: Dynamics of beam
Real structures are made with continuous beams and shells. Beams are the ideal prototype for the demonstration of continuous modes showing clearly that there is no fundamental difference between discrete and continuous dynamic shapes. We solve the essential problem of bended dynamic beam representing for instance a bridge, a wing, a javelin in flight, etc.

General assessment