Aim
The aim of the course is to:

• provide knowledge of the theory of small oscillations of undamped and damped mechanical systems.

• give an understanding of the theory of wave propagation in elastic materials.

Knowledge and understanding
For a passing grade the student must

• be able to give an account of the most important results in the theory of small oscillations in undamped and damped mechanical systems.

• be able to formulate theoretical models for small oscillations in n-degree systems as well as in some simple continuous systems.

• be able to apply modal and transient analysis.

• be familiar with the principles of experimental modal analysis.

Skills and abilities
For a passing grade the student must

• be able to analyse certain simple mechanical systems with the aid of computer programmes (Mathcad, FEM).

• be able to perform an analysis of a vibration problem and to present the results in a well-written report.

• be able to describe some technical problems and possibilities of mechanical vibrations in industrial applications.

Judgement and approach
For a passing grade the student must

• be able to evaluate technical solutions, for instance vibration isolation and damping of vibrations.

• be able to evaluate achieved results based on the problem formulation at hand as well as physical limitations.

Contents
Vibrations in n-degree of freedom systems. Damping mechanisms. Gyroscopic forces. Modal analysis (classical normal modes, complex modes). Transfer functions. Transient response. Continuous systems and wave propagation. Vibration damping and vibration isolation. Applications including the numerical analysis of mechanical vibrations.

Literature
M. Géradin &D. Rixen. Mechanical Vibrations. John Wiley & Sons.
Lidström, P: Lecture notes on Mechanical Vibrations.