FR
EN
Vibrations des structuresGénie mécanique 3 (GSI)
Séquencement
Learning objectives
- Model mechanical oscillating systems of mass-spring-shock absorbers.
- Understand the vibrations of continuous elastic systems.
Prerequisites
| Module | Teaching unit | Semester |
|---|---|---|
| Mathematics 1.1 | Basic Sciences 1 | S1 |
| Point Mechanics | Applied and Industrial Sciences 1 | S1 |
| Mathematics 2.1 | Basic Sciences 2 | S2 |
| Mathematics 2.2 | Basic Sciences 2 | S2 |
| Electrokinetics 2 | Applied and Industrial Sciences 2 | S2 |
| Continuum Mechanics | Mechanical Engineering 1 | S5 |
| Mathematics 3.1 | Basic Sciences 3 | S3 |
| Mathematics 3.2 | Basic Sciences 3 | S3 |
| Mechanics of Solid Systems | Applied and Industrial Sciences 3 | S3 |
| Material Strength | Applied and Industrial Sciences 4 | S4 |
Program
The course is divided into three chapters:
1. Systems with a degree of freedom
1.1 Free vibrations: conservative systems, dissipative systems.
1.2 Harmonic forced response: force-imposed excitement, motion-driven excitement of supports, notions of periodic excitement.
1.3 Transitional response: forced force excitation, motion excitation of supports.
2. Multi-degree systems of freedom
2.1 Two-degree systems of freedom: free vibration and vibration modes, harmonised forced response.
2.2 Systems with several degrees of freedom: vibration modes, principle of modal decomposition, case of dissipative systems, digression on the notion of excitation by motion of supports.
3. Continuous elastic systems
3.1 Longitudinal vibrations of bars: free vibrations and vibration modes, harmonic forced response, principle of modal decomposition, digression on other vibration problems.
3.2 Cross-sectional vibrations of beams: free vibrations and vibration modes, harmonic forced response.
Assessment
For the table exam: a handwritten A4 sheet and a college-type calculator
References
- S. Timoshenko and D. H. Young and W. Weaver (1990), Vibration Problem in Engineering, John Wiley and Sons, Inc.
- K.G. Graff (1991), Wave Motion in Elastic Solids, London, Oxford University Press.
- Mr. Géradin and D. Rixen (1994), Mechanical Vibrations: Theory and Application to Structural Dynamics, Paris, Wiley.
- G. Kelly (2000), Mechanical Vibrations, Theory and Applications, 2nd edition, McGraw-Hill.
- G. Duffy (2015), Green
Skills
4| Ref. | Verb | Description | Level |
|---|---|---|---|
| C1_2 | solve | Establish and resolve the equations of motion from a 1DDL mass-spring system, possibly taking into account damping and harmonic excitation | 2 |
| C2_1 | solve | For a discrete multi-DDL system, know how to establish and solve free and forced motion equations directly or through a modal approach | 3 |
| C2_1 | solve | For a continuous system, establish the equations of motion in the d ́une bar en traction-compression et d ́une beam en flexion | 2 |
| C2_1 | solve | For a continuous system and in the case of a system subject to boundary conditions, express the solutions of the equations of movement (free and forced harmonic) using a modal decomposition | 3 |