Foundation of Structural Dynamics

A course with variable geometry where everyone, we hope, will find personal benefits. The parts can be studied sequentially or independently; and inside each part, elementary learning items can be picked up. Globally, this course proposes a deep knowledge of fundamental dynamics, with possible explicit and implicit applications in structural dynamics, but also in physics and control of any dynamic system (automatics, …). The concepts of static, dynamic, and thermodynamic approaches are defined, followed by the analytical Newtonian foundations of discrete (digital) dynamics. Dynamics is not simply an extension of statics, but another modeling with open possibilities. The basic theorems (Newton‘s equivalence principle, König’ s theorems, conservations) are detailed in the perspective of structural applications. This course opens perspectives towards not only the general dynamics of structures but also towards robotics and control of dynamic systems. These concepts will be learned in a second course (Developments of structural dynamics)

• Understand fundamental theorems of structural dynamics
• Master applications to discrete and digital dynamic systems
• Analyze dynamic systems through mathematical foundations
• Distinguish between dynamics and statics modeling

• Knowledge of point physics, linear algebra, and matrix mathematics
• Basic understanding of solid statics definitions