Advanced Vibrations

General Data
Academic program	Incoming Exchange Student Courses			Module Manager(s) : MAJDOUB Fida
EC Type : Lectures	Advanced Vibrations (LIIExp07EAdvVibrations)
Lab Work : 8h00 Lectures : 16h00 Individual work : 20h00 Total duration: 44h00	Status Obligatoire	Period Semester 7_Mechanical Engineering	Teaching language : English

General objectives
Upon completion of this course, the students are expected to be able to - formulate and solve equations of motion for multi-degree-of-freedom (MDOF) systems using matrix methods. - analyze any vibrational system by simplifying the system - analyze free and forced vibrations of MDOF systems, including damping and nonlinear effects. - apply modal analysis and eigenvalue techniques for system behavior prediction. - interpret physical meaning of vibration modes, natural frequencies, and mode shapes. - understand and analyze continuous systems (e.g. threads) using partial differential equations and separation of variables. - model and simulate vibrational behavior using MATLAB software.

General objectives

Upon completion of this course, the students are expected to be able to
- formulate and solve equations of motion for multi-degree-of-freedom (MDOF) systems using matrix methods.
- analyze any vibrational system by simplifying the system
- analyze free and forced vibrations of MDOF systems, including damping and nonlinear effects.
- apply modal analysis and eigenvalue techniques for system behavior prediction.
- interpret physical meaning of vibration modes, natural frequencies, and mode shapes.
- understand and analyze continuous systems (e.g. threads) using partial differential equations and separation of variables.
- model and simulate vibrational behavior using MATLAB software.

Content
1. Introduction to vibration a. What is vibration b. Industrial issues c. Degrees of freedom of a system d. Reminder stiffness, mass, inertia e. Motion equation for one degree of freedom system 2. Two degrees of freedom system a. Motion equations based on an example b. Matrix notation c. Free motion – Eigenvalues and vectors d. Equations decoupling e. Forced motion 3. Damping – frequency response a. What is damping i. Viscous ii. Structural b. How to model it i. Impact on the equation 4. Vibration isolation and reduction a. Passive isolation b. Active isolation 5. Weighted thread a. Exercise with three degrees of freedom b. Extension of what was seen to continuous system 6. Vibration experiments From measured data to frequency response

Content

1. Introduction to vibration
a. What is vibration
b. Industrial issues
c. Degrees of freedom of a system
d. Reminder stiffness, mass, inertia
e. Motion equation for one degree of freedom system
2. Two degrees of freedom system
a. Motion equations based on an example
b. Matrix notation
c. Free motion – Eigenvalues and vectors
d. Equations decoupling
e. Forced motion
3. Damping – frequency response
a. What is damping
i. Viscous
ii. Structural
b. How to model it
i. Impact on the equation
4. Vibration isolation and reduction
a. Passive isolation
b. Active isolation
5. Weighted thread
a. Exercise with three degrees of freedom
b. Extension of what was seen to continuous system
6. Vibration experiments
From measured data to frequency response

Corequis
General Mechanics; Dynamic; Vibration; Numerical modelling

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