Course details

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Student Mobility > Programmes and Courses > Courses in English > Course details

Dynamics of Multibody Systems

Teaching: Completely taught in English
ECTS: 4
Level: UnderGraduate
Semester: Winter
Prerequisites:
Mechanics II (Solids - Kinematics and Dynamics)
Load:
Lectures Exercises Laboratory exercises Project laboratory Physical education excercises Field exercises Seminar Design exercises Practicum
30 15 0 0 0 0 0 0
Course objectives:
To describe methods, algorithms and application of dynamical and mathematical modelling and computational preparation of dynamical models with the aim of numerical analysis and dynamic simulation of engineering systems with complex kinematical structure and spatial (3D) motion such as robots and manipulators, vehicles, wind-turbines, flight vehicles (with fixed and rotary wings), biomechanical systems and others.
Student responsibilities:
Grading and evaluation of student work over the course of instruction and at a final exam:
Activities that are valued: - written exam 50% - oral exam 50%
Methods of monitoring quality that ensure acquisition of exit competences:
Continuity of students" work will be monitored through activities and exercises in the classroom and through individual and team execution of tasks. Acquired knowledge of students will be monitored through discussions during lectures and exercises. If necessary, the initial level of competence of students will be checked. The quality and success of the course will be monitored through the evaluation at the end of the semester, based on the success of the students at the final exam. Continuous self-evaluation will be done through the comparison of the instructional content of the course with the similar courses at EU universities. Also, the contacts with the professors at EU universities will be organized at regular basis, discussing relevant academic issues.
Upon successful completion of the course, students will be able to (learning outcomes):
After successfully completing the course, the students will be able to: - analyze and apply mathematical models to calculate dynamic response of engineering systems with complex kinematical structure and three-dimensional domain of motion - derive and use mathematical equations for definition of the kinematical constraints of lower and higher kinematic pairs - derive and apply mathematical equations of skleronomic and rheonomic kinematical constraints - use and calculate derived formulations during design of computational models for dynamic analysis and numerical simulation of multibody systems dynamics
Lectures
1. Introduction. Computational dynamics of structural systems: numerical case-studies in mechanical engineering. Elements and structure of mechanical models.
2. Dynamics of rigid bodies: basic equations and princples, Newton-Euler equations. Dynamic equations of 'free' rigid bodies systems.
3. Kinematical constraints, characteristics and principles: scleronomic and rheonomic kinematical constraints, unilateral contacts. Mathematical modelling of kinematical constraints.
4. Kinematical constraint matrix: mathematical structure and characteristics. Kinematical synthesis of mechanical system.
5. Numerical methods of kinematical synthesis.
6. Dynamic equations of constrained multibody systems. Minimal and descriptor form of mathematical model.
7. Computational characteristics of different forms of mathematical model. Numerical methods of reduction of dimensionality of system dynamical equations.
8. Orthogonal-complement matrix: numerical methods, characteristics and utilization principles.
9. Dynamic simulation of multibody structural systems. Preparation of mathematical models for dynamic simulation algorithms.
10. Numerical methods: ODE and DAE systems of differential equations, characteristics and basic principles of time-integration.
11. ODE and DAE systems time-integration schemes.
12. Constraint violation stabilization algorithms. Computational treatment of numerically stiff problems.
13. Computational methods for solving problems of inverse dynamics.
14. Dynamic simulation of systems with variable kinematic structure.
15. Presentation of different case-studies in computational dynamics of structural systems.
Exercises
1. Dynamic analysis and simulation of structural systems: examples of application cases.
2. Basic architecture of computational procedures and program packages: introduction.
3. Basic architecture of computational procedures and program packages: continuation.
4. Numerical case-study assignment: dynamic simulation of structural.
5. Mechanical model synthesis for assigned numerical case: objectives, assumptions, elements of discretization.
6. Definition of kinematical structure of the system. Mathematical modelling of kinematical constraints: introduction.
7. Mathematical modelling of kinematical constraints: continuation.
8. Numerical procedures for the model kinematical synthesis: introduction.
9. Numerical procedures for the model kinematical synthesis: continuation. Redundant kinematical constraints.
10. Computational synthesis of mathematical model of dynamics of the system: introduction.
11. Computational synthesis of mathematical model of dynamics of the system: introduction.
12. Model preparation for the system dynamic simulation.
13. Numerical integration of differential equations of system dynamics: introduction. A choice of numerical method for time-integration. Definition of parameters of integration.
14. Numerical integration of differential equations of system dynamics: continuation. Constraint violation proof-procedure. Results of dynamic simulation.
15. Dynamic simulation with different parameters of integration. Interpretation of the results. Disscussion.
Compulsory literature:
Terze, Z.: Eiber, A. (University of Stuttgart), Introduction to Dynamics of Multibody Systems, FSB Zagreb, e-book, 2002.

Bauchau, O.: Flexible Multibody Dynamics, Willey, 2011.

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Recommended literature:
Eich-Soellner, E.; Fuehrer, C.: Numerical Methods in Multibody Dynamics, B. G. Teub. Stuttgart, 1998.

Faculty of Mechanical Engineering
and Naval Architecture
Ivana Lučića 5
10002 Zagreb, p.p. 102
Croatia
MB 3276546
OIB 22910368449
PIC 996827485
IBAN HR4723600001101346933
tel: +385 1 6168 222
fax: +385 1 6156 940
University of Zagreb
Ministry of Science and Education