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).

• Dynamics?
• Let's get together to the roots of physics. In the beginning, it was dynamics. And dynamics originates all the trunk of the tree of physics. That's the reason why we now analyze the principle of equivalence which allows passing from statics to dynamics.
• Newton!
• Shock and vibration, the heart of dynamics. To fulfill this ambitious program let's dive together into Newton's apple. And let's discover that actually, this free-fall system has revolutionized our vision of physics. So much so this single scientific publication is probably the most cited in the history of science.
• The force is with us.
• To link the cause of motion and motions themselves, it is necessary to parameterize the forces by common denominators i.e. the energies. This bridge is essential to pass from Newton's apple to the real structures. Thus this week constitutes a fundamental transition.
• The light side of the force.
• Some motions occur in the conservative domain, which means that they oscillate, orbit, and circulate in a "perfect" way which is represented by the rails of potential energy. In fact, most of the structures work this way in a first approach. And that's the reason why structural analysis is possible with real modes to represent any structural motion with an excellent approximation (~1%).
• General assessment