Vibrations

General Data
Academic program	ECAM LaSalle Mechanical and Electrical Engineering Programme			Module Manager(s) : MAJDOUB Fida
EC Type : Lectures	Vibrations (LIIEEng06EVibrat)
Tutorials : 4h00 Lab Work : 4h00 Lectures : 12h00 Individual work : 16h00 Total duration: 20	Status	Period Semester 6	Teaching language : English

General objectives
- Recall the method of modal analysis for multi-body systems - Apply modal analysis for one or two degrees of freedom system - Plot and understand a frequency response diagram for a mechanical system - Combine analytical methods and a numerical approach to solve study the vibration of a system - Check consistency of a vibration analysis applied to an industrial case

Content
The course resumes the basics of vibration analysis. At first the vibration analysis and its matrix formalism is presented and applied at two degrees of freedom systems. Then, damping and vibration isolation is presented. Exercises are done after each notion to put into practice formula and method introduced in the course.

Corequis
Before taking this course, students should be able to - Derive a polynomial function of degree n, trigonometric functions and composite functions - Integrate a polynomial function of degree n, trigonometric functions and composite functions - Calculate a scalar and vector product in three dimensions - Project a three-dimensional vector - Apply Newton’s law of motion for a rigid body and a system of rigid bodies - Invert a matrix of dimension 2 or higher - Multiply matrices of dimension 2 or higher

Corequis

Before taking this course, students should be able to
- Derive a polynomial function of degree n, trigonometric functions and composite functions
- Integrate a polynomial function of degree n, trigonometric functions and composite functions
- Calculate a scalar and vector product in three dimensions
- Project a three-dimensional vector
- Apply Newton’s law of motion for a rigid body and a system of rigid bodies
- Invert a matrix of dimension 2 or higher
- Multiply matrices of dimension 2 or higher

Bibliographie
- Pierre Agati, Yves Brémont et Gérard Delville (2003). Mécanique du Solide - Application industrielle 2° éditions : Dunod 302 p. - Serge Viala (2021) Expertise vibratoire – Lecturese material – ECAM LaSalle. - Renaud Bertoni (2022) Vibrations – Lecturese material – ECAM LaSalle. - Luc Gaudiller (2013) Dynamique des solides indéformables - Lectures et exercices. INSA Lyon

Assessment(s)
N°	Nature	Coefficient	Observable objectives
1	Written exam	65	Student must reuse all the concepts seen in class in a final exam.
2		35	Written Report