X. Fang

Granular Damping in Forced Vibration: Qualitative and Quantitative Analyses

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.

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

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.

Damage detection of engine bladed-disks using multivariate statistical analysis

The timely detection of damage in aero-engine bladed-disks is an extremely important and challenging research topic. Bladed-disks have high modal density and, particularly, their vibration responses are subject to significant uncertainties due to manufacturing tolerance (blade-to-blade difference or mistuning), operating condition change and sensor noise. In this study, we present a new methodology for the on-line damage detection of engine bladed-disks using their vibratory responses during spin-up or spin-down operations which can be measured by blade-tip-timing sensing technique. We apply a principle component analysis (PCA)-based approach for data compression, feature extraction, and denoising. The non-model based damage detection is achieved by analyzing the change between response features of the healthy structure and of the damaged one. We facilitate such comparison by incorporating the Hotellings statistic T2 analysis, which yields damage declaration with a given confidence level. The effectiveness of the method is demonstrated by case studies.

A highly efficient discrete element approach for granular damping analysis

Granular damping is a technique of achieving high structural damping with granules embedded within or attached to the vibrating structure. The discrete element method (DEM), which is based on the direct dynamic analysis of all granules using Newtons equations, can accurately predict the granular damping behavior. However, the numerical implementation of such approach is complicated and the key issue is the time-consuming granule contact detection in DEM. In this research, a new computational scheme is presented for granular damping analysis using DEM. Instead of using the straightforward search over all granular pairs, the link cell (LC) method is used to find the candidate pairs for possible contacts, which performs contact check of a granule only with the neighbor granules. To further reduce the number of candidate pairs, a Verlet table is incorporated with the LC method which lists all granular pairs whose distances are less than a threshold distance dt. The Verlet table for candidate pairs can be updated in an adaptive manner, corresponding to the dynamic states of the vibrating system. Collectively, these improvements can increase the computational efficiency of DEM by multiple times as compared to the state-of-the-art.

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

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.

Analysis of Granular Damping Using Hilbert Transform Based Technique

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.Copyright

Analysis of Segregation Phenomenon in Granular Motion

Over the past decade, many studies have been carried out to investigate one of the unique phenomena in granular materials: vibration-induced segregation in granular mixture, i.e., under vertical vibration, larger granules rise to the top even without density difference with other granules. However, the mechanisms behind this phenomenon are not yet completely understood. In this study, the discrete element method (DEM) is used for the numerical analysis of the granular segregation in a vertically vibrating container. We systematically investigate the rising time of an intruder inside the granular mixture as a function of the granular size, density, depth, and the vibrating frequency and amplitude. Our studies show that the segregation phenomenon is caused by a variety of mechanisms within different vibration regimes. Under weak vibration, segregation is driven by the geometrical effect and inertia. Under moderate vibration, segregation can be enhanced dramatically with the occurrence of convection. Under strong vibration where the granular material becomes fluidized, the buoyancy or sinkage of granules prevails and segregation may be suppressed.Copyright

Granular Damping Analysis Using a Direct Simulation Monte Carlo Approach

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 Newtons 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.Copyright

Damage detection by statistical analysis of vibration signature

This paper studies damage detection using structural frequency response functions (FRFs). In practice, one major difficulty of using FRFs for damage detection is that the vibration signatures are inevitably contaminated by noise. Sensitivity to detect damage is severely impaired as abnormality information caused by the damage could be covered up by the relatively high measurement noise. To tackle this issue and to develop a robust damage detection protocol, a feature extraction/de-noising methodology based on principal component analysis (PCA) is implemented. We first establish a feature space of the intact structure by using multiple measurements with noise. Abnormal signature that is different from the baseline signature can then be identified and magnified after signal reconstruction using intact structure features. Essentially, the directionality between an inspected signal and the baseline signal in the feature space is used as index of damage occurrence. Numerical examples demonstrate that, in all cases considered, the new methodology has good accuracy and high sensitivity for structural damage detection. The relation between detectability, damage severity, noise level, and the number of data sets of the intact structure is examined.

Learning Rate Effect in Neural Network for Damage Detection

Neural network is a powerful tool that can be utilized for structural damage detection and health monitoring. Since damage usually varies/reduces stiffness, frequency response variation can be used as indicator for damage occurrence. A well designed neural network can correlate frequency response variation to damage localization/severity without resorting to detailed structural modeling. While various neural network based approaches have been developed, their effectiveness, efficiency, and robustness oftentimes rely on the selection of several important parameters in the network construction. One of the key performance metrics for a neural network is the learning rate. Although the dynamic steepest descent algorithm (DSD) and fuzzy steepest descent algorithm (FSD) have shown promising possibility of improving the learning convergence speed significantly without increasing the computational effort, its performance still depends on the selection of control parameters and control strategy. In this paper, a tunable steepest descent algorithm (TSD) improving the performance of the dynamic steepest descent algorithm is proposed. A numerical benchmark example shows that the proposed algorithm significantly improves the convergence rates of the backpropagation algorithm. A structural health monitoring system incorporated with the neural network trained by the adaptive learning algorithm is developed for detecting the impact damage.Copyright