Analysis of time-varying mechanical systems using the method of impulsive parametric excitation

Abstract

In this contribution, dynamical systems with time-varying parameters are described by a set of difference equations using the method of impulsive parametric excitation. It is shown that this description allows to get a detailed insight into the effect of time-varying parameters to the modal energy content of mechanical systems and enables to analyze mechanical systems, but also to apply parametric excitation in order to affect the energy content of mechanical systems in a desired manner. It is demonstrated with a simple example, that therewith a prediction of the required parametric excitation to transfer energy across modes of vibration and/or to extract energy from mechanical systems is possible, which results in a much faster decay of vibrations compared to the case where only natural damping is present.