Waves in mechanics

Continuum mechanics (1^st year Mechanics course)

•  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

•  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

•  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

•  CC1: Reports on practical works (50%)
•  CC2: Scientific report on a given subject (50%)

•  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.

•  Bruno Cochelin
•  Daniel Mazzoni