Advanced Vibrations

Données Générales
Programme Académique	ECAM LaSalle Mechanical and Electrical Engineering Programme			Responsable(s) Module : MAJDOUB Fida
Type d'EC : Cours	Advanced Vibrations (LIIEEng07EAdvVibrations)
TP : 8h00 Cours : 18h00 Travail personnel : 21h00 Durée totale: 47h00	Status	Periode Semester 7	Langue d'enseignement : English

Objectifs Généraux
The students should be able to: - describe the relationship between the properties of mass, stiffness and damping of a system with one degree of freedom and its frequency response, - determine by calculation the modal characteristics of a system with two degrees of freedom and to interpret the results of this calculation, - to use the principle of modal superposition methods, - to describe the relationship between the modal characteristics of a multi-degree of freedom system and its frequency response, - to explain the principles and limitations of the equipment used to measure the frequency response of a mechanical system, - to use the principle of an experimental modal analysis and to define the necessary measures for this analysis.

Objectifs Généraux

The students should be able to:
- describe the relationship between the properties of mass, stiffness and damping of a system with one degree of freedom and its frequency response,
- determine by calculation the modal characteristics of a system with two degrees of freedom and to interpret the results of this calculation,
- to use the principle of modal superposition methods,
- to describe the relationship between the modal characteristics of a multi-degree of freedom system and its frequency response,
- to explain the principles and limitations of the equipment used to measure the frequency response of a mechanical system,
- to use the principle of an experimental modal analysis and to define the necessary measures for this analysis.

Contenu
The presentation of the relations between the physical properties of a mechanical system and its vibratory behavior is carried out in the form of lectures on the following points: 1 - Vibration of a system with one degree of freedom: Conservative System: Free Movement - Clean Pulsation - Kinetic Energy and Deformation Energy. Non-conservative system: Viscous damping model - Frequency response - Resonance. 2 - Vibrations of discrete systems with n degrees of freedom: Modes of vibration - Calculation of modal characteristics - Decoupling of equations of motion - Proportional damping model - Modal superposition - Frequency response - Experimental modal analysis. 3 - Vibration reduction methodology: Vibration isolation - Modification of a natural frequency - Increase of the damping - Use of a dynamic dampener granted

Contenu

The presentation of the relations between the physical properties of a mechanical system and its vibratory behavior is carried out in the form of lectures on the following points:

1 - Vibration of a system with one degree of freedom:
Conservative System: Free Movement - Clean Pulsation - Kinetic Energy and Deformation Energy.
Non-conservative system: Viscous damping model - Frequency response - Resonance.

2 - Vibrations of discrete systems with n degrees of freedom:
Modes of vibration - Calculation of modal characteristics - Decoupling of equations of motion - Proportional damping model - Modal superposition - Frequency response - Experimental modal analysis.

3 - Vibration reduction methodology:
Vibration isolation - Modification of a natural frequency - Increase of the damping - Use of a dynamic dampener granted

Prérequis
General Mechanic; Dynamic; Vibration; Numerical modelling

Bibliographie
Recommended reference: Kelly, S. G. (2008). Advanced engineering mathematics with modeling applications. CRC Press.

Évaluation(s)
N°	Nature	Coefficient	Objectifs
1	Written exam	0,55	The students are assessed on the different concepts learnt in class in their final exam.
2	Project	0,45	The students are given 3 real applications. They are required to simplify the system, analyze the vibrational behavior, and recommend some enhancements to the system.
3	Lab	0,1	The students are provided with projects having real-life applications. They are required to analyze it and try to improve it.