A Direct Simulation Monte Carlo Approach for the Analysis of Granular Damping

Abstract

Granular damping, which possesses promising features for vibration suppression in harsh environments such as in turbo-machinery and spacecraft, has been studied using empirical analysis and more recently using the discrete element method (DEM). The mechanism of granular damping is nonlinear and, when numerical analyses are employed, usually a relatively long simulation time of structural vibration is needed to reflect the damping behavior. The present research explores the granular damping analysis by means of the direct simulation Monte Carlo (DSMC) approach. Unlike the DEM that tracks the motion of granules based upon the direct numerical integration of Newton’s equations, the DSMC is a statistical method derived from the Boltzmann equation to describe the velocity evolution of the granular system. Since the exact time and locations of contacts among granules are not calculated in the DSMC, a significant reduction in computational time/cost can be achieved. While the DSMC has been exercised in a variety of gas/granular systems, its implementation to granular damping analysis poses unique challenges. In this research, we develop a new method that enables the coupled analysis of the stochastic granular motion and the structural vibration. The complicated energy transfer and dissipation due to the collisions between the granules and the host structure and among the granules is directly analyzed, which is essential to damping evaluation. Also, the effects of granular packing ratio and the excluded volume of granules, which may not be considered in the conventional DSMC approach, are explicitly incorporated in the analysis. A series of numerical studies are performed to highlight the accuracy and efficiency of the new approach.