Course syllabus

# Flerkroppsdynamik Multibody Dynamics

## FMEN02, 7,5 credits, A (Second Cycle)

Valid for: 2015/16
Decided by: Education Board E
Date of Decision: 2015-04-13

## General Information

Elective for: BME4-br, F4, F4-tf, F4-bem, M4-bem, Pi4-bem
Language of instruction: The course will be given in English

## Aim

The aim of the course is to:

• provide knowledge of the basic theory of the dynamics of multibody systems consisting of rigid bodies as well as simple flexible bodies.
• give insight in the numerical analysis of the equations of multibody dynamics.

## Learning outcomes

Knowledge and understanding
For a passing grade the student must

• be able to give an account of the most important results in the theory of multibody dynamics.
• be able to formulate theoretical models for systems of connected rigid bodies and simple elastic bodies.
• have knowledge of the commercial computer programmes that are available.

Competences and skills
For a passing grade the student must

• be able to analyse certain simple multibody systems with the aid of computer programmes (Mathcad, FEM, MBS-programmes).
• be able to perform an analysis of a multi-body system and to present the results in a well-written report.
• be able to describe some technical problems in industrial applications that can be studied with multibody dynamics.

Judgement and approach
For a passing grade the student must

• be able to evaluate achieved results based on the problem formulation at hand as well as physical limitations.

## Contents

Rigid body kinematics and dynamics; Euler angles,etc, inertia tensor, Euler equations, Energy and Effect. Fixed-axis rotation; reaction forces, dynamic balancing, stability, Gyroscopic movement.d'Alemberts principle. Lagranges equations; constraints, degrees of freedom, Lagrange function, generalized forces.Multibody systems; holonomic and non-holonomic constraints,contact forces, friction, loss of effect. Lagranges equations with constraints. Rigid and flexible bodies in systems;discretization and coordinate representation mass- and stiffness-matrices. Equations of motion, construction and numerical treatment.Computer programmes; ADAMS, Matlab.

## Examination details

Assessment: Hand in exercises and written exam.

• Basic courses in Mechanics, Linear Algebra and Calculus

The number of participants is limited to: No
The course overlaps following course/s: FMEN01, FME071, FME120

• Lidström P., Nilsson K.:Lecture Notes on Fundamentals of MultiBody Dynamics. Division of Mechanics, LTH, 2006.
• A.A. Shabana: Dynamics of MultiBody Systems. 3rd Edition. Cambridge University Press.2005.

## Contact and other information

Course coordinator: Univ. lekt. Per Lidström, per.lidstrom@mek.lth.se
Course homepage: http://www.mek.lth.se
Further information: The course might be offered in English.