2021-2022 / MECA0029-1

Theory of vibration


26h Th, 26h Pr, 30h Proj.

Number of credits

 Master of Science (MSc) in Aerospace Engineering5 crédits 
 Master of Science (MSc) in Mechanical Engineering (EMSHIP+, Erasmus Mundus)5 crédits 
 Master of Science (MSc) in Mechanical Engineering (EMSHIP+, Erasmus Mundus)5 crédits 
 Master of Science (MSc) in Engineering Physics5 crédits 


Jean-Claude Golinval

Language(s) of instruction

English language

Organisation and examination

Teaching in the first semester, review in January


Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

This course provides a solid background in vibration theory for engineering applications.
Course outline

  • Introduction and analytical dynamics of discrete systems
  • Undamped vibrations of n-degree-of-freedom systems
  • Damped vibrations of n-degree-of-freedom systems
  • Continuous systems: bars, beams and plates
  • Approximation of continuous systems by displacement methods; Rayleigh-Ritz and finite element method
  • Solution methods for the eigenvalue problem
  • Direct time-integration methods
  • Introduction to nonlinear dynamics

Learning outcomes of the learning unit

The objective of the course is to focus on analytical and computational methods for predicting the dynamic response of practical engineering structures. Special attention is devoted to aerospace, mechanical and civil engineering structures.

Prerequisite knowledge and skills

This course requires basic knowledge of fundamental calculus and differential equations. The course also requires a mastery of introductory dynamics and mechanics.

Planned learning activities and teaching methods

One project is assigned to the students. It will give hands-on practice with methods used in structural dynamics (e.g., the finite element method, Newmark's algorithm, component mode synthesis).

Mode of delivery (face to face, distance learning, hybrid learning)

Face-to-face course

Recommended or required readings

M. Géradin, D. Rixen
Mechanical Vibrations - Theory and Application to Structural Dynamics.
John Wiley & Sons, 2015
ISBN 978-1-118-90020-8

Assessment methods and criteria

Exam(s) in session

Any session

- In-person

written exam ( open-ended questions ) AND oral exam

Written work / report

Additional information:

The final grade will be based on the project report, its oral presentation and a written exam on the theory:
1. The project has to be done individually or by group of maximum 2 students. The grade will be based on the results and the quality of the report (scientific and technical content, conciseness, structuring of the written report and clarity of the text). An oral presentation will be organised at the end of the project.
2. The written exam will consist in answering to questions on the theoretical concepts explained during the lectures. No document is allowed for the written exam.
The assessment is based on the weighted geometric average of the project and the written exam. The final note is calculated as follows:
Final note = (Project)^(0.6) * (Theory)^(0.4)
There is no partial exemption in case of failure.

Work placement(s)

Organizational remarks

The organisation is presented in details during the first lecture.


Jean-Claude Golinval (JC.Golinval@uliege.be)
Assistant : Olivier Devigne (O.Devigne@uliege.be)