A comprehensive investigation of granular damping

Granular damping is a passive vibration suppression technique which attenuates the response of a vibrating structure by the use of a granule-filled enclosure attached to or embedded in the structure. The underlying principle of granular damping is the removal of vibratory energy through inelastic collisions and frictional interactions among the granules and between the granules and the enclosure. Although simple in concept, the mechanisms of granular damping are very complicated and its performance depends on a number of factors, such as vibration level, granular material properties, and enclosure dimensions, etc. The first task of this dissertation is to develop advanced simulation methodology for granular damping analysis. Two numerical simulation approaches: the discrete element method (DEM) based on Molecular Dynamics (that is suitable for accurate analysis with moderate number of granules) and the direct simulation Monte Carlo (DSMC) method derived from the Boltzmann equation (that is suitable for a very large number of granules), are developed to analyze structural vibrations with granular damping.^ The energy dissipation of granular damping is resulted from a combination of several different loss mechanisms including the momentum exchange, impact restitution, and friction. The second task of this dissertation is to perform correlated analytical modeling and numerical studies to evaluate each energy dissipation mechanism qualitatively and quantitatively. The analytical approximate model based on the multi-phase flow theory is established for the description of granular motion inside the damper, which accounts for the complete effects of collisions/impacts and dynamic frictions in a granular damper.^ The performance of granular damping is dependent on vibration level (i.e., vibration amplitude and frequency), especially in transient vibrations. It is challenging to interpret granular damping characteristics in transient vibration, as both the vibration frequency and the damping capacity may have significant changes over time. Therefore, the third task of this dissertation is to employ a new signal processing method, called the Hilbert-Huang transform (HHT), to study the dependency of nonlinear granular damping characteristics, such as vibration frequency and damping ratio, on the vibration level. The damping characteristic extracted through HHT analysis can be integrated into practical analysis tools such as finite element method for structural vibration analysis.^ Overall, this dissertation presents a comprehensive investigation of granular damping by a series of numerical and analytical approaches and experimental studies. These new and efficient tools can provide design guidelines of granular dampers for practical application.