EXPERIMENTAL STUDY OF ENERGY ABSORPTION PROPERTIES OF GRANULAR MATERIALS UNDER LOW FREQUENCY VIBRATIONS

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1 International Journal of Modern Physics B Vol. 18, Nos (2004) c World Scientific Publishing Company EXPERIMENTAL STUDY OF ENERGY ABSORPTION PROPERTIES OF GRANULAR MATERIALS UNDER LOW FREQUENCY VIBRATIONS HU MAO-BIN, KONG XIANG-ZHAO and WU QING-SONG School of Engineering Science, University of Science and Technology of China, Hefei , P. R. China qswu@ustc.edu.cn ZHU ZHEN-GANG Lab of Internal Friction and Defects in Solids, Inst. Solid State Phys., Chinese Acad. Sci., P.O. Box 1129, Hefei , P. R. China Received 31 August 2003 The low frequency vibration energy absorption properties of granular materials have been investigated on an Invert Torsion Pendulum (ITP). The energy absorption rate of granular material changes nonlinearly with amplitude under low frequency vibration. The frequency of ITP system increases a little with granular materials in the holding cup. The vibration frequency of ITP system does not change with time. Keywords: Granular materials; energy absorption. 1. Introduction Understanding the behavior of granular materials is a challenging task and has attracted considerable interests. 1 Among them, the phenomena induced by vibration are peculiarly fascinating, such as jamming, 2 segregation 3 5 and surface waves, 6 where granular materials behave according to the vibration parameters and dissipate energy through inelastic collisions. In this essay, we investigated vibration energy absorption behavior of granular materials. By changing experimental parameters (frequency, amplitude, time), the granular energy absorption (dissipation) rates variation has been measured. Corresponding author. 2708

2 Experimental Study of Energy Absorption Properties Experimental Set-Up and Specimens Our experiments were conducted on an Invert Torsion Pendulum (ITP), which was invented by TS Ke. 7 The apparatus set-up is shown in Fig. 1. We design the holding cup and stirring cylinder for the measurement. The lower part of the stirring cylinder is immersed in granulates and provides torsion motion, while other modes are reduced. When the stirring cylinder is driven to a specified angular deflection and released, it will oscillate in simple harmonic motion and attenuate to zero due to the granular energy absorption and the system s natural dissipation. Maximum angular deflections A n of each vibrations are measured from the gauge. We can also add some weight to the ends of driving rod to adjust the system s vibration frequency. The energy absorption rate can be calculated by: Q 1 = δe 2πE = A2 n A 2 n+1 2πA 2 n = 1 ( ) 1 A2 n+1 2π A 2. (1) n Five kinds of granular materials are used in our experiments: glass beads of diameter d g = mm, and plastic beads of diameter d g = mm, mm, mm, mm. The size of granulates is uniformly distributed. We first measured the background energy dissipation rate Q 1 0 without granular materials, and then the energy absorption rate Q 1 1 with granular materials in the holding cup. Ignoring the nonlinear coupling of granular absorption with Fig. 1. Apparatus for granular energy absorption rate measurement: 1. weight, 2. weak suspension, 3. reflect mirror, 4. driving rod, 5. couple of frequency-adjust weight, 6. couple of driving coil, 7. lamp unit with blade slit, 8. gauge, 9. pendulum rod, 10. stirring cylinder, 11. holding cup, 12. granular specimen, 13. torsion wire, 14. bottom.

3 2710 M.-B. Hu et al. background dissipation, the granular energy absorption rate Q 1 can be calculated by: 3. Results Q 1 = Q 1 1 Q 1 0. (2) In our experiment, different granular materials show qualitatively same properties. We found something special in the granular material: (i) The vibration energy absorption rate changes nonlinearly with driving amplitude. And this tendency appears with different vibration frequencies. Some results of d g = mm glass beads is shown in Fig. 2. Here the horizontal coordinate denotes the amplitude of torsion turning measured from the gauge. We note that the absorption rate of small amplitude is almost ten times of that of large amplitude. We have examined 21 driving frequencies for every type of granular materials in our experiments and found qualitatively the same tendency. (ii) The vibration frequency of ITP system increases with granulates in the holding cup. For example, the frequency increases as much as 0.46 Hz with d g = mm glass beads, as shown in Table 1. Here we adjust the system s vibration frequency by adding some weight to the ends of driving rod. (iii) The vibration frequency of torsion pendulum does not change with time, as shown in Fig. 3. The slope of the curvature (or period) does not change with time. Fig. 2. Absorption-amplitude profile of glass beads (d g = mm).

4 Experimental Study of Energy Absorption Properties 2711 Table 1. Comparison of system vibration frequency (Hz). Without glass beads With glass beads Frequency increment Fig. 3. Time series for a plastic beads (d g = mm) experiment. 4. Conclusion In conclusion, the low frequency energy absorption properties of several granular materials have been investigated. The granular materials energy absorption rate varies nonlinearly with vibration amplitude. Granular materials can also affect ITP system, because the system s vibration frequency increases with granular materials in the holding cup. However, the system s vibration frequency does not change with time. These phenomena are unique for granular materials. We think our results may provide some inspirations for the understanding of some granular collective behaviors where energy dissipation plays an essential role. Acknowledgments This project was supported by the National Natural Science Foundation of China under Grant No

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