Contribution
Self-similarity of free vibration decays in cantilever beams
* Presenting author
Abstract:
Free vibrations decay according to a power law in cantilever beams after impact excitation. Power laws are self-similar – an aspect that has so far been of little importance in linear vibration analysis methods. This presentation will briefly introduce the notion of self-similarity and will explain how the self-similar property of a free vibration decay can enhance our physical understanding of damping in materials. We propose an extended stress-strain relation that is based on Boltzmann's »Theorie der elastischen Nachwirkung«, and investigate how it affects the decay of free vibrations in beams. Free vibrations in a cantilever beam are measured using laser Doppler vibrometry. They are decomposed into empirical modes, and analysed using the Hilbert-Huang spectrum. The Hilbert-Huang Transform combines an empirical mode decomposition with Hilbert spectral analysis. It is a signal processing technique that can adapt to a given dataset without strict a-priori assumptions. This makes the Hilbert-Huang transform a suitable method for the analysis of non-linear or non-stationary signals. However, mode mixing, computational demands and sensitivity to noise must carefully be managed.