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.
Upon completion of the course students should be 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
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.
Active participation, lab report, test
All registered students will be distributed in teams - please sign up for the course if you want to take it.