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| MECA0029-1 | Mechanical Vibrations
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| Duration : | 30h Th, 30h Pr |
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| Credits/ECTS : |
| civil engineering in physics, 2nd year | | | | 6 |
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| civil engineering in physics (programme for "licenciés" in physics sciences), 1st year | | | | 5,5 |
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| Master in Aerospatial Engineering, in-depth approach, 1st year | | Toute l'année | | 5 |
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| Master in Mechanical Engineering, in-depth approach, 1st year | | Toute l'année | | 5 |
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| Master in Civil Ingineering, specialized approach, 1st year | | Toute l'année | | 5 |
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| Master in Mechanical Engineering, specialized approach, 1st year | | Toute l'année | | 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 engineering structures. The course first focuses on analytical mechanics (Hamilton's principle and Lagrange's equations) to derive the equations of motion of single-degree-of-freedom, multi-degree-of-freedom, and continuous systems. The application of the finite element method to vibrating structures is also reviewed and illustrated with simple examples. Different methods for solving eigenvalue problems and for numerical integration of ordinary differential equations are then discussed. Finally, the course 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.
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 : | Two projects will be assigned during the course of the semester. The grade will be calculated based on the final written reports and the oral presentation. Each of the assignments covers a specific aspect of vibration theory and gives 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 : | Two projects will be assigned during the course of the semester. The grade will be calculated based on the final written reports and the oral presentation |
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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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