ECTS credits
2 credits
Semester
Fall
Prerequisites
Learning objectives
• Discover the wide range of common phenomena related to waves and vibrations
• Be able to understand dynamic phenomena in mechanics (solid, fluid and acoustic)
• Know how to distinguish between the notions of wave and vibration and know the formalisms involved
• Master the basic theoretical tools related to these notions
• Know how to use numerical tools to solve different types of problems
Description of the programme
• Lecture review and introduction to wave and vibration phenomena in different media
• Introduction of the time dimension in continuum mechanics and consequences
-- Notion of wave
-- Wave formalism
-- Different types of wave equations and solutions
• Introduction of boundary conditions
-- Standing waves, vibrations
-- Eigenmodes
• Tools and methods
-- Buckingham's Pi theorem and applications
-- Fourier transform, DFT, Shannon criterion
-- CFL condition
• Introduction to nonlinear acoustics
-- Constitutive equations in the nonlinear non-viscous case
-- Constitutive equations in the viscous nonlinear case
-- Applications of nonlinear acoustics
Generic central skills and knowledge targeted in the discipline
• Know how to model dynamic problems
• Know how to identify the characteristic parameters of a problem
• Know how to define the methodology to solve a dynamic problem
• Know how to identify complex dynamic phenomena such as instability or chaos
How knowledge is tested
• CC1: Reports on practical works (50%)
• CC2: Scientific report on a given subject (50%)
Bibliography
• Billingham, J., & King, A. (2001). Wave Motion (Cambridge Texts in Applied Mathematics). Cambridge: Cambridge University Press. doi:10.1017/CBO9780511841033
• G. B. Whitham, “Linear and Nonlinear Waves,” John Wiley & Sons Inc., Hoboken, 1999. doi:10.1002/9781118032954
• Sirven, Les ondes : du linéaire au non linéaire, Dunod, 1999.
Teaching team
• Bruno Cochelin
• Daniel Mazzoni
- Total hours of teaching24h
- Master class8h
- Directed work8h
- Practical work8h