The course is offered in English and corresponds to the German course "Dynamik der Mehrkörpersysteme".
Creating Models for Technical Systems
Vibration models are especially needed in mechanical systems: e.g. to be able to build controllers for active suspension systems. In the lectures of vibration technology you learn how to build multi-body models for real systems which are as simple as possible and still consider all significant effects.
Also, an efficient method to determine planar and spatial kinematics of general moving multibody systems is presented as well as methods to form the equations of motion by using the Lagrange-Equation or the Newton-Euler-Equation. The second order equation of motion can be transformed to an equivalent first order equation of state.
Analysis of Technical Systems
The equations of motion and states are mathematical models of systems and are valuable tools to get secure information on parameter influences and parameter optimization especially in dealing with dynamic systems. In vibration technology you learn how to solve the equations of motion and states with the help of matrix calculus to analyse multibody systems.
Eigenvalues and eigenvectors are calculated to analyze the intrinsic behavior. They give information on vibration amplitudes and frequencies as well as on the decay of free oscillations. In addition, stability statements are based on simple eigenvalue stability criteria. The lectures of vibration technology teach you how to do necessary calculations by hand or with the help of computer programs.
Technical systems often perform forced vibrations. You learn how to solve non-homogeneous state and motion equations of specific excitation functions. During the operation of technical systems periodic excitations occur, for example because of unbalanced forces or occurring wave-like movements. In such cases, critical excitation frequencies or drive speeds and the frequency-dependent system behavior need to be calculated. Another special excitation function is the step function excitation, e.g. in form of a run over the curb. The vibration response to such impulse functions are often used to compare and evaluate vibration systems and can easily be calculated with the equation of state.
A very wide range of practice-relevant analysis of movements can be covered by the previously introduced special solution methods which gives closed solutions for state and motion equations. But general forms of excitation require the calculation of the general equation of the non-homogeneous state equation. This is often only numerically possible and meaningful. Therefore the lecture deals with the numerical aspects to solve the equations of state with the help of fundamental matrices.