After successful completion of the course, students are able to:

• derive the free oscillation eigenvalue problem and interpret its results, i.e. model shapes and natural frequencies, as well as be familiar with the most important numerical solution methods
• derive reduced order models for multi degree of freedom systems by using an appropriate modal basis
• conduct harmonic response analyses of full and reduced systems, incorporating different damping methods, and be familiar with the concept of transfer functions
• describe the working principles of measurement equipment for experimental modal analysis, and to use such equipment in practice
• extract natural frequencies and mode shapes from measurement data by using various identification techniques, as well as compare experimentally determined modes to computational results based on appropriate criteria

Additionally, students should improve their ability to

• work in teams
• learn with and from other students
• present their findings in a clear and concise manner

Students are introduced to the concept of computational modal analysis based on the example of mechanical systems. Modal reduction techniques for the derivation of efficient computational models are discussed. Furthermore, knowledge about measurement methods for the experimental determination of modal parameters (experimental modal analysis) of mechanical structures will be acquired.

Starting form a mathematical description of a linear mechanical system (e.g. obtained by the finite element method) the free oscillation eigenvalue problem is introduced. The solutions, natural frequencies and oscillation modes, are the basis for modal analysis. The following topics with respect to computational modal analysis will be covered:

• Eigenvalue problem(s)
• Solution methods
• Modal basis & model reduction

In addition to computational modal analysis, measurement techniques can be used to experimentally determine the modal parameters of mechanical systems. The appropriate theory including frequency response functions, fast Fourier transform, etc. is introduced. Furthermore, modern measurement systems (laser scanning interferometer) and modal analysis software packages will be used in laboratory experiments.

The course is thematically divided into 5 consecutive sections. Each section is accompanied by an introductory theory lecture. The theory is then applied to practical problems in the exercise phase and prepared for the concluding workshop. Here the results are presented and discussed. The example problems are supported by extensive templates, and exercises on the topics of experimental modal analysis are carried out with measurement data.

Grading is based on the submissions of exercise problems (from the 5 exercise parts), the active participation in the workshops, as well as a final test.

All registered students will be distributed in teams - please sign up for the course if you want to take it.