Dynamique et vibrationsE.A. Mécanique et énergétique 2 (MRI)

The objectives of this module are:

1. introduce Lagrangian formalism, detail the strategy to analyze the stability of simple dynamic systems around existing balances.
2. know how to determine the temporal and frequency response of discrete stable systems in response to a release experiment or in the case of harmonic vibrations, using a projection on a modal basis, and know how to plot its general appearance.

Mechanics of STPI 1A Mechanics of STPI 2A Solids Systems Dynamics of STPI 2A Pre-Oriented Solid Systems

This course is divided into two parts. Chapter 1: General mechanics, balance and stability

• Equations of mechanics by Newtonian and Lagrangian approaches; Mondre Principle Action
• Elaboration of the equations of movement by the equations of Lagrange
• Analysis of the existence of equilibrium positions
• Analysis of the stability of small movements around balances where appropriate

Chapter 2: Linear vibrations of mechanical systems

• Oscillator 1 degree of freedom: free oscillations and forced vibrations (harmonic forcing and general case)
• Oscillator 2 degrees of freedom: clean modes, free oscillations and forced vibrations (harmonic forcing and general case), direct resolution or modal basis.
• Identification of parameters equivalent to a continuous structure by a Rayleigh Ritz approach.
• Continuous system vibrations: strings and beams.

1 final exam without document, with calculator.

• De Langre, E. et Chaigne , A., "Dynamic and Vibration", Palaiseau: ed. de l'École polytechnique DL 2008
• Axisa, F., "Modeling of mechanical systems. Volume 1, Discreet Systems", Paris, Hermès Science Pub. 2001
• Gignoux, C., Silvestre-Brac, B., "Mechanical corrected problems and course summaries: from Lagrange to Hamilton", Grenoble Sciences, Les Ulis: EDP Sciences DL 2004