Mechanical vibrations - 3EUAVSM8
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Goals
Provide basic notions required for the mechanical design of rotating machines for energy production.
Introduction to the theory of vibrations:
- Obtain and solve the equations of motion in simple cases and for small (linear) oscillations around equilibrium
- Understand the concepts of eigenfrequencies and eigenmodes
- Obtain eigenmodes and eigenfrequencies of discrete systems with n degrees of freedom
Content 1- One efficient method for solving the equations of motion (20h)
Description of the motion of a mechanical system using generalised coordinates
Equations of motion (energy method)
Linearisation of the equations of motion
Free and forced oscillations of a one-degree-of-freedom system
Eigenfrequencies, eigenmodes
Vibration of systems with several degrees of freedom
2- numerical intégration of the equations of motion (8h + 22h practicals)
Deriving eigenfrequencies and eigenmodes for n-DOFs systems
Programming with python
PrerequisitesBasics of mathematics - differential equations, Taylor series, linear algebra
Tests 2h exam (DS) + assignment (CC)
CC 1/3 + CT 2/3
Bibliography Seto, Mechanical Vibrations, Schaum's outline series, McGraw Hill, 1964
Landau, Lifchitz, Mécanique, Editions Mir 1966
Lalanne, Berthier, Der Hagopian, Mécanique des vibrations linéaires, Masson, 1986
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Date of update July 12, 2018