Study Programmes 2015-2016
MECA0029-1  
Theory of vibration
Duration :
30h Th, 30h Pr, 30h Proj.
Number of credits :
Master in aerospace engineering (120 ECTS)5
Master in mechanical engineering (120 ECTS)5
Master in physical engineering (120 ECTS)5
Master in physical engineering (120 ECTS)5
Lecturer :
Jean-Claude Golinval
Language(s) of instruction :
English language
Organisation and examination :
Teaching in the first semester, review in January
Units courses prerequisite and corequisite :
Prerequisite or corequisite units are presented within each program
Course 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 course :
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 will be 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) :
face-to-face
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 :
The final grade will be based on the project report and the oral exam:
1. Group of students will be assigned a project. 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 oral exam will consist in answering to questions on the theoretical concepts explained in the course.
The assessment is based on the weighted geometric average of the project and the oral exam. The final note is calculated as follows:
Final note = (Project)^(0.6) * (Theory)^(0.4)
Work placement(s) :
Organizational remarks :
Contacts :
Jean-Claude Golinval (JC.Golinval@ulg.ac.be)
Mathieu Bertha (Mathieu.Bertha@ulg.ac.be)
Items online :
MECA0029 - Theory of vibration
Copy of the slides.
MECA0029 - Theory of vibration (Project assignment)
You will find here all the documents related to the fulfillment of each part of the project.