Universal response of optimal granular damping devices

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.

Download Full-text

Investigation of Granular Damping in Transient Vibrations Using Hilbert Transform Based Technique

Journal of Vibration and Acoustics ◽

10.1115/1.2827454 ◽

2008 ◽

Vol 130 (3) ◽

Cited By ~ 9

Author(s):

X. Fang ◽

H. Luo ◽

J. Tang

Keyword(s):

Hilbert Transform ◽

Damping Ratio ◽

Temporal Frequency ◽

Nonlinear Damping ◽

Vibration Level ◽

Damping Characteristics ◽

The Difference ◽

The Hilbert Transform ◽

Granular Damping ◽

The Impact

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, packing ratio, etc. In this study, free vibration experiments 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 the vibration level. This HT based analysis can produce an effective 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 and the advantages of granular damping. Finally, the validity of the proposed approach is also examined by the successful prediction of vibration response using the extracted granular damping characteristics.

Download Full-text

Granular Damping in Forced Vibration: Qualitative and Quantitative Analyses

Journal of Vibration and Acoustics ◽

10.1115/1.2203339 ◽

2006 ◽

Vol 128 (4) ◽

pp. 489-500 ◽

Cited By ~ 39

Author(s):

X. Fang ◽

J. Tang

Keyword(s):

Vibration Suppression ◽

Damping Effect ◽

Numerical Studies ◽

Highly Nonlinear ◽

Wide Range ◽

Suppression Technique ◽

Parametric Studies ◽

Quantitative Analyses ◽

Underlying Mechanisms ◽

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. While promising in many applications especially under harsh conditions, the granular damping mechanism is very complicated and highly nonlinear. In this paper, we perform correlated analytical modeling and numerical studies to evaluate qualitatively and quantitatively the energy dissipation in granular damping. First, an improved analytical model based on the multiphase flow theory is developed for the description of granular motion inside the damper, which accounts for the complete effects of collisions/impacts and dynamic frictions among the granules and between the granules and the enclosure. This model can efficiently characterize the damping effect with high fidelity over a very wide range of parameters, and thus can be used to develop guidelines for parametric studies. With this as a basis, detailed numerical studies using the discrete element method are also carried out to analyze the underlying mechanisms and then provide mechanistic insight for granular damping. In this paper, we focus our attention on the granular damping effect on forced vibrations, which has potential application to a variety of systems.

Download Full-text

Granular Damping Analysis Using a Direct Simulation Monte Carlo Approach

Applied Mechanics ◽

10.1115/imece2006-14448 ◽

2006 ◽

Author(s):

X. Fang ◽

J. Tang

Keyword(s):

Monte Carlo ◽

Direct Simulation Monte Carlo ◽

System Optimization ◽

Numerical Analyses ◽

Structural Vibration ◽

Computational Time ◽

Granular System ◽

Direct Simulation ◽

Simulation Monte Carlo ◽

Granular Damping

Granular damping, which possesses promising features for vibration suppression in harsh environment, has been studied using empirical analysis and more recently using the discrete element method (DEM). The mechanism of granular damping is highly nonlinear, and, when numerical analyses are performed, usually a relatively long simulation time of structural vibration is needed to reflect the damping behavior especially at low frequency range. 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 using the direct numerical integration of Newton's equations, the DSMC is a statistical approach 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 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 and accurately incorporated into the analysis, which is essential to damping evaluation. Also, the effects of granular packing ratio and the excluded volume of granules, which may not be included in conventional DSMC method, are explicitly taken into account in the proposed approach. A series of numerical analyses are performed to highlight the accuracy and efficiency of the new approach. Using this new algorithm, we can carry out parametric analysis on granular damping to obtain guidelines for system optimization.

Download Full-text

A highly efficient discrete element approach for granular damping analysis

10.1117/12.658751 ◽

2006 ◽

Cited By ~ 1

Author(s):

X. Fang ◽

J. Tang

Keyword(s):

Discrete Element ◽

Highly Efficient ◽

Element Approach ◽

Granular Damping

Download Full-text

Analysis of Granular Damping Using Hilbert Transform Based Technique

Volume 1: 21st Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C ◽

10.1115/detc2007-34900 ◽

2007 ◽

Author(s):

X. Fang ◽

H. Luo ◽

J. Tang

Keyword(s):

Hilbert Transform ◽

Damping Ratio ◽

Temporal Frequency ◽

Nonlinear Damping ◽

Vibration Level ◽

Damping Characteristics ◽

The Difference ◽

The Hilbert Transform ◽

Granular Damping ◽

The Impact

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.

Download Full-text