Course code: wb1418

Course name: Engineering Dynamics

This concerns a Course

ECTS credit points: 3

Faculty of Mechanical Engineering and Marine Technology

Section of Engineering Mechanics

Lecturer(s): Daniel J. Rixen

Tel.:  015 - 27 1523 /      

Catalog data:

dynamical systems, stability, mode superposition, solid mechanics, equations of motion, continuous system, discretization, Finite Elements, harmonic response, mechatronics, vibrations

Course year:

MSc 1^st year

Course language:

English

In case of Dutch: Please contact the lecturer about an English alternative, whenever needed.

Semester:

1A / 1B

Hours per week:

2

Other hours:

16

Assessment:

Oral exam

Assessment period:

1B / 2A

(see academic calendar)

Prerequisites (course codes):

Statics and Strength of materials (e.g. wb1214), Dynamics (e.g. wb1311), Linear Algebra 

Follow up (course codes):

Engineering Dynamics and Mechanicsms (wb1419, extension of wb1418), Multibody Dynamics A (wb1310), Multibody Dynamics B (wb1413), Numerical Methods in Dynamics (wb1416), Non-Linear Vibrations (wb1412).

Detailed description of topics:

The dynamic behavior of structures (and systems in general) plays an essential role in engineering mechanics and in particular in the design of controllers. In this master course, we will discuss how the equations describing the dynamical behavior of a structure and of a mechatronical system can be set up. Fundamental concepts in dynamics such as equilibrium, stability, linearization and vibration modes are discussed. Also an introduction to discretization techniques to approximate continuous systems is proposed.

The course will discuss the following topics:

- Review of the virtual work principle and Lagrange equations

- linearization around an equilibrium position: vibrations

- elastodynamics in a solid and  continuous systems

- discretization techniques (Rayleigh-Ritz and Finite Elements)

- Free vibration modes and modal superposition

- Forced harmonic response of non-damped and damped structures

Other advanced topics relevant to mechanical engineering will be covered if time permits and depending on the interest of the students: basics of rotor dynamics, non-linear vibrations, random vibrations, prestressed structures, electromechanical and piezoelectric systems.

Course material:

•  Lecture notes (available through blackboard)

References from literature:

• Mechanical Vibrations, Theory and Application to Structural Dynamics, M. Géradin and D. Rixen, Wiley, 1997.
• Applied Dynamics, with application to multibody and mechatronic systems, F.C. Moon, Wiley, 1998, isbn 0-471-13828-2.
• Engineering vibration, D.J. Inman, Prentice Hall, 2001, isbn 0-13-726142-X
• The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, T.J.R. Hughes Prentice-Hall, 1987.
• Structural Dynamics in Aeronautical Engineering, M.N. Bismark-Nasr, AIAA education series, 1999, isbn 1-56347-323-2

Remarks assessment, entry requirements, etc.:

An assignment will be given which will make up part of the final mark. SInce the enphasis of the lectures will be on understanding concepts in dynamics more than memorizing formulas, the oral exam will be open book to evaluate your understanding of the concepts.

Learning goals:

The student must be able to:

1. explain the relations between the principle of virtual work and the Lagrange equations for dynamics to the basic Newton laws

2. describe the concept of kinematic constraints (holonomic/non-holonomic, scleronomic/rheonomic) and choose a proper set of degrees of freedom to describe a dynamic system

3. write the Lagrange equations for a minimum set of degrees of freedom and extend it to systems with additional constraints (Lagrange multiplier method)

4. linearize the dynamic equations by considering the different contributions of the kinetic and potential energies (both for system with and without overall motion imposed by scleronomic constraints)

5. analyze the linear stability of dynamic systems (damped and undamped) according to their state space formulation if necessary

6. explain and use the concept of free vibration modes and frequencies

7. interpret and apply the orthogonality properties of modes to describe the transient and harmonic dynamic response of damped and undamped systems

8. evaluate the approximations introduced when using truncated modal series (spatial and spectral)

9. explain how mode superposition can be used to identify the eigenparamters of linear dynamic systems

10. write the dynamic equations of a continuum using local equilibrium or energy approaches, including the proper boundary conditions

11. find an approximate solution to linear continuous problems by Rayleigh-Ritz methods and Finite Elements (bars and beams)

12. describe the virtual work principle for continuous systems and show the link to the minimum residual interpretation and to Rayleigh-Ritz approximations

Computer use:

The assignement will require using Matlab-like software.

Laboratory project(s):

-

Design content:

-

Percentage of design:  -0%