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| MECA0029-1 | Mechanical Vibrations
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| Duration : | 30h Th, 30h Pr |
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| Credits/ECTS : |
| Master in Aerospatial Engineering, in-depth approach, 1st year | | Premier quadrimestre | | 5 |
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| Master in Mechanical Engineering, in-depth approach, 1st year | | Premier quadrimestre | | 5 |
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| Master in Engineering Physics, in-depth approach, 2nd year | | Premier quadrimestre | | 5 |
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| Master in Aerospace Engineering, Professional Focus (Management), 1st year | | Premier quadrimestre | | 5 |
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| Master in Mechanical Engineering, specialized approach, 1st year | | Premier quadrimestre | | 5 |
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| Holder(s) : | Gaëtan Kerschen |
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| Language : | Langue française |
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| Course contents : | This course provides a solid background in vibration theory. Students learn analytical and computational methods for predicting the dynamic response of practical engineering structures. Special attention is devoted to aerospace, mechanical and civil engineering structures. The course also offers a gentle introduction to the difficult, but fascinating, world of nonlinear oscillations.
Course outline (14 two-hour lectures + several practice exercises):
1. Introduction and analytical dynamics of discrete systems (1 lecture)
2. Undamped vibrations of n-degree-of-freedom systems (2 lectures)
3. Damped vibrations of n-degree-of-freedom systems (2 lectures)
4. Continuous systems: bars, beams and plates (2 lectures)
5. Approximation of continuous systems by displacement methods; Rayleigh-Ritz and finite element method (2 lectures)
6. Solution methods for the eigenvalue problem (1 lecture)
7. Direct time-integration methods (2 lectures)
8. Introduction to nonlinear dynamics (2 lectures) |
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| Course objective : | 1. To teach students to model and analyze free and forced vibration of single and multi-degree-of-freedom lumped element systems.
2. To introduce students to the modeling and analysis of continuous vibrational systems including approximate solution methods (e.g., the finite element method).
3. To introduce students to nonlinear structural dynamics. |
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| Prerequisites : | This course requires basic knowledge of fundamental calculus and differential equations. The course also requires a mastery of introductory dynamics and mechanics. Familiarity with Matlab is desirable. |
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| Workshops : | One project will be assigned during the course of the semester. It will give hands-on practice with methods used in structural dynamics (e.g., the finite element method, Newmark's algorithm, component mode synthesis). |
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| Organization : | 1st Semester |
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| Assessment : | The final grade will be based on the project report and the oral exam:
1. Group of two students will be assigned a project. The grade will be based on the results and the quality of the report.
2. During the oral exam, the students will have to show a solid knowledge of the different chapters and methods. A special attention will be devoted to the understanding of the different concepts. No mathematical proofs will have to be demonstrated. The oral exam will also include the individual presentation of the project report. It will comprise three sequences:
- Questionnaire with 10 questions : 25 minutes.
- Presentation of the project report : 10 minutes.
- Discussion: 15 minutes.
In addition, several quizzes (with 10 questions each) will be assigned after the lessons. The dates and number of quizzes will not be known to you. If the average of the quiz grades is greater than the average of the grades of the oral exam and of the project report, then the quizzes will count 30% toward the final grade. Participation is optional.
Student assessment criteria:
- Oral exam and project report: 60% and 40%.
- Oral exam, project report and quizzes: 40%, 30% and 30%.
September exams: same terms, but, if the grade of the project report is below 12/20, the student will be assigned a new project. |
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| Contacts : | Gaetan Kerschen
g.kerschen@ulg.ac.be |
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| Items online : |
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| Copy of the slides |
| A copy of the slides used during the lectures is available at the URL address here below. |
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