Analysis of Granular Damping Using Hilbert Transform Based Technique

Abstract

Granular damping results from a combination of energy dissipation mechanisms including the impact and the friction between the vibrating structure and granules and among the granules. Although simple in concept, granular damping is very complicated and its performance depends on a number of factors, such as vibration level, granular material properties, and packing ratio, etc. In this study, free vibration tests are conducted on a cantilevered beam incorporated with granular damping. A signal analysis approach based on the Hilbert transform (HT) is then employed to identify the nonlinear damping characteristics from the acquired responses, such as the dependency of the natural frequency and damping ratio on vibration level. This HT based analysis can produce an accurate temporal-frequency amplitude/energy analysis which provides us with physical insights of the nonlinear transient response. A direct comparison between the granular damping and the impact damping (with single impactor to dissipate vibratory energy) is performed to highlight the difference between these two as well as the advantages of granular damping. Finally, validity of the proposed approach is also examined by the successful prediction of vibration response using the extracted granular damping characteristics.