Students are enabled to develop task-specific computational models for analyzing vibrations in machines and vehicles, to interpret vibration phenomena from a physical perspective, and to experimentally determine dynamic parameters.

Content:

1. Introduction: Vibrations in mechanical engineering

2. Free linear vibrations with multiple degrees of freedom: Mode shapes and modal representation

3. Forced linear vibrations with multiple degrees of freedom: Frequency response, resonance, damping, modal representation

4. Fourier Analysis of Vibrations: Fourier series, Discrete Fourier Transform (DFT), Fast Fourier Transform (FFT)

5. Free vibrations of one-dimensional continua: Models, solutions to the one-dimensional wave equation, bending vibrations of beams

6. Forced vibrations of one-dimensional continua: Direct solutions, modal solutions

7. Vibration identification: Single-degree-of-freedom and multi-degree-of-freedom systems

8. Approximation methods: Spatial discretization, method of weighted residuals, d'Alembert-Lagrange principle, trial (shape) functions

9. Discretization of simple continua using the Finite Element Method (FEM): FEM steps, axial and torsional vibrations of rods, bending vibrations of beams

10. Reduction of degrees of freedom (condensation): Static, modal, and mixed condensation

Recommended Literature:

Woernle, C.: Manuskript zur Vorlesung Technische Schwingungslehre (Foliensatz). 
Gasch, R.; Knothe, K.; Liebich, R.: Strukturdynamik; Springer Vieweg, 2012.