||Dr.ir. P. Tiso
|Contact Hours / Week x/x/x/x:
||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).
|Expected prior knowledge:
||Statics and Strength of materials (e.g. wb1214), Dynamics (e.g. wb1311), Linear Algebra
||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. If time permits, 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
- Free vibration modes and modal superposition
- Forced harmonic response of non-damped and damped structures
||The student is able to select different ways of setting up the dynamic equations of mechanical systems, to perform an analysis of the system in terms of linear stability and vibration modes and to properly use mode superposition techniques for computing transient and harmonic responses.
More specifically, 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
||The assignement will require using Matlab-like software.
|Literature and Study Materials:
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
||written exam + oral exam + assignment
||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.