Mechanical Vibrations

The course studies the time dependent behavior of structures and systems excited by dynamic forces. The course starts with the analysis of systems with one, two and several degrees of freedom, with and without damping, and also deals with simple continuous structures (beams and bars) and more complex finite element models. The different sources of excitations for practical applications are described, together with a description of the effects and a discussion of possible design and remedial measures. Sensors, data acquisition and signal processing to measure vibrations experimentally are also presented.

The students will learn how to model time dependent dynamic behavior of structures. Emphasis is put on the ability to derive simple models from real complex structures and to compute their dynamic response due to different types of excitations.

The students will also develop a deep understanding of the sources and effects of vibrations on structures, as well as basics on instrumentation and methods to measure vibration levels, frequency response functions, and extract modal data on real structures.

When measured or predicted vibration levels are excessive, the students will learn what are the most relevant redesign and remedial measures and how to apply them, with a design oriented approach.

The course is articulated around different case studies for which the students will learn to describe the source of excitation, how to model the problem and predict vibration levels, as well as propose the most adequate design and remedial measures when these levels are excessive.

The course consists of 24h of lectures based on the principle of flipped classes. The students are asked to watch one or several short videos before the class, and the time in the class is dedicated to interactive activities such as wooclap sessions, group exercises and discussions about case studies to consolidate the theoretical knowledge.

The following topics are covered:

1. Introduction
2. One degree of freedom systems
3. Sources of vibrations
4. Multiple Degree of Freedom systems
5. Finite elements models
6. Continuous Systems
7. Equivalent SDOF systems
8. Flow induced vibrations
9. Vibrations problems
10. Dynamic response computation
11. Design and remedial measures
12. Damping
13. Tuned vibration absorbers
14. Vibration isolation
15. Vibration testing and modal analysis

The exercise sessions are organized in 6 sessions (24h) using Jupyter Notebooks (Python). Exercise sessions will conclude with an individual project (12h) to be performed at home, which is defended individually during the oral examination.

The exercises are aimed at illustrating the theoretical concepts and to prepare for the final project: understanding of the excitation (based on Fourier analysis), modeling of the physical system (including reduction to a single degree of freedom system), computation of the response both in time and frequency domain, assessment of potential dynamic instabilities

The following topics are covered in the exercise sessions:

• One degree of freedom systems and general introduction
• Multiple degree of freedom systems and mode shapes
• Fourier Analysis and excitation sources
• Reduction to SDOF systems
• Vortex induced vibrations and flutter
• Dynamic response computation in time and frequency domain

Contribution au profil d'enseignement

This teaching unit contributes to the following competences:

• In-depth knowledge and understanding of exact sciences with the specificity of their application to engineering
• Reformulate complex engineering problems in order to solve them (simplifying assumptions, reducing complexity) 
• Correctly report on research or design results in the form of a technical report or in the form of a scientific paper
• Present and defend results in a scientifically sound way, using contemporary communication tools, for a national as well as for an international professional or lay audience

Références, bibliographie et lectures recommandées

Inman, D.J - Engineering vibrations. Prentice Hall, 3d Edition, 2007
Géradin M., Rixen D. Mechanical Vibrations - Theory and Application to Structural Dynamics. John Wiley & Sons, second edition, 1997

Support(s) de cours

• Podcast
• Syllabus

Contacts

Arnaud Deraemaeker (arnaud.deraemaeker@ulb.be), Wout Weijtens (wout.weijtjens@vub.be)

Campus

Solbosch

Méthode(s) d'évaluation

• Projet
• Examen oral

Projet

Examen oral

Timely submission of all 6 completed exercise sessions through the designated portal is required and accounts for 20% of the final mark. The oral examination is split in two parts, a first part with questions related to the theoretical part of the course, and a second part dedicated to the defense of the individual project. Each part accounts for 40% of the total mark.

Construction de la note (en ce compris, la pondération des notes partielles)

20% for the exercise sessions, 80% for the oral examination (40% for each part).

Langue(s) d'évaluation

• anglais