Structural Dynamics

General Data
Academic program	General Engineering Program			:
Type d'EC	Classes (LIIAem08EDynStr)
Lectures : 26h00 Lab Work : 8h00 Total duration : 54h00	Status :	Period : ACADEMIC SEMESTER	Education language : French

Learning Outcomes
- Recall specific technical vocabulary of kinematic and dynamic of rigid bodies as well as for the vibration of generic bodies. - Apply the method associated with the study of the dynamic of rigid bodies - Determine the accelerations and the forces acting on solids in multi-body mechanisms - Recall the method of modal analysis for multi-body systems - Apply modal analysis for two degrees of freedom system - Calculate kinematics and dynamics parameters using software for rigid bodies - Combine analytical methods and a numerical approach to solve multi-body rigid dynamic problems - Check consistency of a dynamical study applied to an industrial case

Learning Outcomes

- Recall specific technical vocabulary of kinematic and dynamic of rigid bodies as well as for the vibration of generic bodies.
- Apply the method associated with the study of the dynamic of rigid bodies
- Determine the accelerations and the forces acting on solids in multi-body mechanisms
- Recall the method of modal analysis for multi-body systems
- Apply modal analysis for two degrees of freedom system
- Calculate kinematics and dynamics parameters using software for rigid bodies
- Combine analytical methods and a numerical approach to solve multi-body rigid dynamic problems
- Check consistency of a dynamical study applied to an industrial case

Content
The course resumes the basics of rigid body mechanic before introducing less common notions such as shocks theory and vibration analysis. The movement is studied independently of its causes first. The kinematic and the associated torsor are introduced. The course focus and the point before extrapolating the results to generic solids. Mechanical actions and their modelling is presented in order to apply the dynamic notions. Newton's laws are introduced et allow to link the movement to it cause. Energy is approached as well as the basics of shock theory, which is at the limit of the rigid body hypothesis. Finally, the vibration analysis and it matrix formalism is presented and applied at two degress of freedom systems. Exercises are done after each notion to put into practice formula and method introduced in the course.

Content

The course resumes the basics of rigid body mechanic before introducing less common notions such as shocks theory and vibration analysis.
The movement is studied independently of its causes first. The kinematic and the associated torsor are introduced. The course focus and the point before extrapolating the results to generic solids.
Mechanical actions and their modelling is presented in order to apply the dynamic notions.
Newton's laws are introduced et allow to link the movement to it cause.
Energy is approached as well as the basics of shock theory, which is at the limit of the rigid body hypothesis.
Finally, the vibration analysis and it matrix formalism is presented and applied at two degress of freedom systems.
Exercises are done after each notion to put into practice formula and method introduced in the course.

Pre-requisites / co-requisites
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 - Use a torsor and its transport properties for calculation - Invert a matrix of dimension 2 or higher - Multiply matrices of dimension 2 or higher

Pre-requisites / co-requisites

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
- Use a torsor and its transport properties for calculation
- Invert a matrix of dimension 2 or higher
- Multiply matrices of dimension 2 or higher

Bibliography
- Pierre Agati, Yves Brémont et Gérard Delville (2003). Mécanique du Solide - Application industrielle 2° éditions : Dunod 302 p. -Gérard Colombari, Jaques Giraud (2005). Sciences industrielles pour l'ingénieur : Foucher 384 p. -Jean-Dominique Mosser, Jacques Tanoh, Pascal Leclerq (2010). Sciences industrielles pour l'ingénieur : Dunod 263 p. - Luc Gaudiller (2013) Dynamique des solides indéformables - Cours et exercices. INSA Lyon

Bibliography

- Pierre Agati, Yves Brémont et Gérard Delville (2003). Mécanique du Solide - Application industrielle 2° éditions : Dunod 302 p.
-Gérard Colombari, Jaques Giraud (2005). Sciences industrielles pour l'ingénieur : Foucher 384 p.
-Jean-Dominique Mosser, Jacques Tanoh, Pascal Leclerq (2010). Sciences industrielles pour l'ingénieur : Dunod 263 p.
- Luc Gaudiller (2013) Dynamique des solides indéformables - Cours et exercices. INSA Lyon

Assessment(s)
N°	Nature	Coefficient	Observable objectives
1	2 hours exam without calculator or documents. Generals formulas are given at the end of the subject. Everything seen in the lecture needs to be known.	2	Check students' knowledge of technical vocabulary and evaluate their ability to use course content to solve simple problems.
2	Synthesis of the practical work activities to send 24h after ythe end of the session. 1 to 2 pages maximum	1	Check students' ability to correctly use simulation software, understand the influence of modeling parameters, interpret the results of calculations and resume it in a report.