Dynamique des systèmesPO MRI 2 (STPI)

Understand and master models to describe oscillating movements of mechanical structures and constructions. Three parts are discussed: 1/ Balance and stability of mechanical systems. In this section, equations of movement of unformable solid systems will be established and the existence and stability of equilibrium positions will be analyzed. 2/ Oscillations and vibrations of discrete mechanical systems This section focuses on the temporal and frequent resolution of systems with 1 or 2 degrees of freedom. Under the condition of harmonic forcing, the concept of mechanical resonance will be seen. For 2 degrees of freedom systems one will calculate the own modes. 3/ Vibration risk To determine whether the vibrations experienced by an operator endanger their health.

1- Dynamics, Balance and Stability

• Dynamics of solids and solid systems,
• Energy Theoremes
• movement equation
• Linearization of motion equations
• Approach to the dynamics of systems deformable by discrete models, 2- Oscillations and vibrations
• Harmonic or cushioned oscillator model
• Resolution in time : transformed from Laplace
• Frequent domain resolution: Harmonic and Fourier-transformed loading
• Oscillator N degrees of freedom (applications to N=2)
• Concept of own mode, calculation of own frequencies and deformities 3- Vibration risk
• Discreet model of the human body
• Standards for vibration risk
• Health implications
• Calculation of daily exposure acceleration

Continuous monitoring: 2 exams 50% each during the module.

• B. Combes, Vibration of structures for engineer and technician, Ellipses2009.
• Mr. Pedro and P. Pahud, Vibration Mechanics, Presses Polytechniques romandes, 2003.