Dynamic of multibody systems

Recommended Prerequisites

Applied Mechanic; Mathematics; algebra and numerical methods.

Teaching Methods

he theoretical contents of the curricular unit will be presented through lectures illustrated with practical cases. Students are encouraged to apply the competences acquired through practical activities associated with the training of using multibody program, including the analysis and discussion of results. The sharing of professional experience will be encouraged during these activities.

Learning Outcomes

This course aims to accelerate the innovation process, to reduce development costs and increase the quality of engineering products. Using the multi-body simulation methods, is possible to evaluate the project performance and reduce the number of prototypes, avoiding unpleasant surprises in the development cycle, and providing quick responses to last-minute project changes. At the end of this course unit students may be able to:

1) Identify and define the concept of multibody system;

2) Define the several coordinate types, kinematic constraints and equations of motion of constrained multibody systems;

3) Create and use a commercial program that allows multi-body systems simulations with the computation of generalized coordinates and forces.

4) Critically analyse the numerical results and try to find alternative solutions.

Work Placement(s)

No

Syllabus

Introduction to the fundamental concepts of multibody systems: a) Reference systems; b) Particle mechanics; c) Mechanics of rigid bodies; d) constrained movement.

2. Formulation and Dynamic analysis of rigid multibody systems: a) kinematic of a rigid body in Cartesian coordinates; b) equations of motion of rigid body systems; c) equations of motion of multibody systems.

3. Solution of equations of motion of multibody systems: redundant constraints.

4. Numerical integration of the equations of motion:

5. control of the constraint’s violation: Baumgarte stabilization method; Augmented Lagrange formulation; Coordinate partitioning method.

6. Formulation and analysis of examples of application of multibody systems: slider-crank; Four-bar mechanism.

7.Equations of motion of flexible multibody systems

Head Lecturer(s)

Maria Augusta Neto

Assessment Methods

Assessment
Resolution Problems: 30.0%
Exam: 70.0%

Bibliography

[1] Shabana,A. A., Dynamics of multibody systems, Third Edition, Cambridge University Press 2005.

[2] Nikravesh, P. E., Computer Aided Analysis of Mechanical Systems, Prentice-Hall, Englewood Cliffs, New Jersey, 1998.

[3] Neto, M. A., Optimização de sistemas dinâmicos multicorpo flexíveis em materiais compósitos, Universidade de Coimbra, Março de 2006. https://ap1-dev.uc.pt/handle/10316/1985.

[4] Neto, M.A.; Amaro, A.; Roseiro, L.; Cirne, J.; Leal, R., Engineering computation of structures: the finite element method. Springer, 2015