Foundation of Structural Dynamics

Foundation of Structural Dynamics

Instructor: Yves Gourinat

What you'll learn

Understand the basic theorems of structural dynamics and their implications toward complex systems.
Master their applicability to discrete systems and applications to digital modeling in dynamics.

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Assessments

5 assignments

Taught in English

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There are 5 modules in this course

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).

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.

What's included

2 videos3 readings1 assignment4 discussion prompts

2 videosTotal 11 minutes

Welcome to the course6 minutesPreview module
Dynamics: a definition4 minutes

3 readingsTotal 40 minutes

Welcome to the course15 minutes
Glossary15 minutes
Dynamics: kinematics is not dynamics10 minutes

1 assignmentTotal 40 minutes

Quiz about dynamics40 minutes

4 discussion promptsTotal 40 minutes

Who are we?10 minutes
Vector and energies10 minutes
What is dynamics?10 minutes
Discuss10 minutes

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.

What's included

5 videos2 readings2 assignments

5 videosTotal 16 minutes

Illustration: balloon explosion in slow motion0 minutesPreview module
Illustration: the fall of the Tacoma bridge in 19402 minutes
The apple and the moon6 minutes
Energetical law2 minutes
Vectorial law4 minutes

2 readingsTotal 20 minutes

Summary10 minutes
Newton and the moon10 minutes

2 assignmentsTotal 60 minutes

Few questions about Shock and vibration illustrations15 minutes
Some questions on Newton45 minutes

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.

What's included

3 videos3 readings1 assignment

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%).