## Dynamics of Mechanical Systems

Module number: MW1421

Duration: 1 Semester

Recurrence: Winter semester

Language: English

Number of ECTS: 5

## Staff

Professor in charge: Daniel Rixen

## Amount of work

Class attendance: 45

Private Study: 105

Total: 150

## Course work and exam formalities

Final written examination (90 minutes) or oral (depending on the number of attendees). The final exam will count for 70% of the final grade. 30% of the final grade will be determined by a modelling project (using a commercial Finite Element tool) the students have to work on during the semester

## Description

The course is intended to give a broad overview of essential aspects of dynamics in engineering systems (including important aspects for electro-mechanical engineers).

The following topics will be discussed:

• basics of analytical dynamics (virtual work principle and Lagrange equations)
• elements of dynamics of rigid body systems
• introduction to vibration analysis fo structures (eigenmodes, forced harmonic response)
• elements of rotordynamics
• introduction to elastodynamics and Finite Element discretization
• multiphysical coupling: electrostatic forces, piezoelectric effect, vibroacoustics, thermomechanics

## Learning outcome

This course is intended for

• students that do not have mechanical engineering as main focus but need to understand the basics of engineering dynamics (for instance Electrical or Power Engineering students)
• or mechanical engineering students interested in understanding topics beyond the BSc level, for instance  elements of rotor dynamics or multiphysical coupling.

At the end of the module the students understand the essence of the virtual work principle in dynamics and the Lagrangian formalism for deriving equations of motion for mechanical systems. They are able to apply  this method to create mathematical models describing the dynamics of simple systems of points and of a rigid body. The student will be able to linearize the dynamic equations, compute eigenmodes and apply mode superposition to compute the forced response to harmonic excitations. The student will be able to derive the equations of motion of simple rotor systems and will understand the concept of stability and resonance in those systems. The student will understand the basic equations of elastodynamics and the basics of the finite element discretization method. The student will understand how the dynamics of structures interacts with forces originating from other physical sources such as electrostatic, piezo-electric, acoustic and thermic. He will be able to apply commercial Finite Element software to solve simple problems involving one of those physical couplings.

## Prerequisites

Undergraduate level engineering mechanics and mathematics:

- basic kinematics and dynamics

- linear algebra and differential calculus

## Literature

M. Géradin and D. Rixen. Mechanical Vibrations, Theory and Application to Structural Dynamics, Wiley & Sons, Chichester, 3d edition, 2015

Pfeiffer, F., & Schindler, T. (2015) Introduction to Dynamics, Springer

T. J. Hughes. The finite element method: linear static and dynamic finite element analysis. DoverPub-lications, com. 2012

R.. D. Cook, D. S. Malkus, M. E. Plesha and R. J. Witt. Concepts and Applications of Finite Element Analysis (4. Edition). Wiley, 2002, ISBN 0-471-35605-0

## Teaching and studying methods

lecture, tutorial