Number of hours
- Lectures 14.0
- Projects 0
- Tutorials 14.0
- Internship 0
- Laboratory works 22.0
ECTS
ECTS 2.5
Goal(s)
Provide basic notions required for the mechanical design of rotating machines for energy production.
1- Introduction to the theory of vibrations:
Introduce Lagrange equations and solve the equations of motion in simple cases and for small oscillations around equilibrium
2- Linear elasticity of solid bodies:
Understand concepts of stress and strain
Introduce linear elastic consitutive law
Understand the concept of elastic criterion
Structural design using a finite-element method program
Content(s)
1- Introduction to the theory of vibrations:
1- One efficient method for solving the equations of motion
Description of the motion of a mechanical system using generalised coordinates
Principle of virtual power and Lagrange equations
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
2- Linear elasticity of solid bodies:
1- Basics of the theory of elasticity
Stress
Strain
linear elastic constitutive law
Mises limit criterion
2- Structural design in elasticity
Introduction to a finite-element program, mesh, boundary conditions
Comparison with analyticam solutions of simple problems, torsion, bending, traction, shear
Principal stresses and strains
Design exercices - Mises limit criterion
Prerequisites
Basics of mathematics - volume and surface integrals, differential equations, Taylor series, vector analysis, linear algebra
Test
2h exam + assignment
2/3 DS + 1/3 CC
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
French State controlled diploma conferring a Master's degree
