本研究以活塞式顆粒阻尼實驗結果及具阻尼顆粒箱體彈簧系統實驗結果驗證多體動力學(Multi-body dynamic, MBD)與離散元素法(Discrete element method, DEM)雙向耦合模擬技術理論，並探討不同腔體大小與腔體配置對箱體振動行為的影響。研究結果顯示，本研究提出的雙向耦合模擬結果與對應實驗結果吻合良好。在活塞式顆粒阻尼實驗中，主要是由顆粒摩擦機制控制系統的能量消散。具顆粒體之箱體相較於未挖空箱體皆
有明顯的減振效果，在改變腔體大小但固定系統質量相等情形下，減振效果依序為 1/4箱體、1/8 箱體與 1/16 箱體。在改變腔體配置但固定系統質量相等情形下，減振效果依序為具一層腔體、兩層腔體與三層腔體之箱體。加入顆粒體於箱體中，不會影響加速度的運動週期，但可降低加速度振幅，達到減振效果。

The purpose of this study is to validate the two-way coupled simulation based on Multibody dynamics and Discrete element method using two sets of experiment, including particlebased thrust damper test and free vibration test of small devices with particle damper, dash-pot and spring. This study further investigates the effect of size and layout of particle damper on dynamic characteristics. Results show that the coupled MBD-DEM simulations agree well with the corresponding experiments. In the loading scenario of particle-based thrust damper, friction mainly controls the energy dissipation of the mechanical system. It is evident that particle damper significantly reduces vibration. Under the same mass but with different sizes of particle damper, the attenuation effect follows the sequence: 1/4 box＞1/8 box＞1/16 box. Under the same mass but with different layouts of particle damper, the attenuation effect follows the sequence: one-chamber＞double chamber＞triple chamber. Adding the damping particles to the system does not affect the period of the acceleration, but reduces the acceleration amplitude.

[1] H.V. Panossian, Structural damping enhancement via non-obstructive particle damping technique, J. Vib. Acoust. 114 (1992) 101-105.
[2] T. Chen, K. Mao, X. Huang, M.Y. Wang, Dissipation mechanisms of non-obstructive particle damping using discrete element method, Smart. Structure. Mat. 4331 (2001) 294-301.
[3] K. Mao, M.Y. Wang, Z. Xu, T. Chen, Simulation and Characterization of Particle Damping
in Transient Vibrations, J. Vib. Acoust. (2004) 126.
[4] M.R. Duncan, C.R. Wassgren, C.M. Krosgrill, The damping performance of a single particle impact damper, J. Sound. Vib. 286 (2005) 123-144.
[5] W. Liu, G.R. Tomlinson, J.A. Rongong, The dynamic characterization of disk geometry
particle dampers, J. Sound. Vib. 280 (2005) 849-861.
[6] Z. Lu, X. Lu, H. Jiang, S. F.Masri, Discrete element method simulation and experimental validation of particle damper system, Int. J. Comp. Aid. Eng. S. 31 (2014) 4.
[7] W.Q. Xiao, Y.X. Huang, H. Jiang, H. Lin, J.N. Li, Energy dissipation mechanism and experiment of particle dampers for gear transmission under Centrifugal Loads, Particuology. 27 (2016) 40-50.
[8] P.A. Cundall, O.D.L. Strack, A discrete numerical model for granular assemblies, Geotechnique. (1979) 47-65.
[9] C. O’Sullivan, J.D. Bray, Selecting a suitable time step for discrete element simulations that use the central difference time integration scheme, Eng. Computation. 21 (2004) 278-303.
[10] K. Mao, M.Y . Wang, Z. Xu, T. Chen, DEM simulation of particle damping, Powder Technol. 142 (2004) 154-165.
[11] C.X. Wong, M.C. Daniel, J.A. Rongong, Energy dissipation prediction of particle dampers, J. Sound. Vib. 319 (2009) 91-118.
[12] Z. Lu, S.F. Masri, X. Lu, Parametric studies of the performance of particle dampers under harmonic excitation, Struct. Control. Hlth. 18 (2009) 79-98.
[13] MSC.Software: Using ADAMS/Solver. Mechanical Dynamics,Inc., Ann Arbor, Michigan, 1997.
[14] J.B. McConville, J.F. McGrath, Introduction to ADAMS Theory. Mechanical Dynamics Inc, Michigan, 1998.
[15] A.A. Shabana, Dynamics of Multibody Systems, 3rd edn.Cambridge University Press, Cambridge, 2005.
[16] W. Schiehlen, Computational dynamics: theory and applications of multibody systems, Eur. J. Mech. A/Solids. 25(4) (2006) 566–594.
[17] P. Flores, J. Ambrósio, J.C.P. Claro, H.M. Lankarani, Kinematics and Dynamics of Multibody Systems with Imperfect Joints, Springer. (2008).
[18] L.X. Xu, An approach for calculating the dynamic load of deep groove ball bearing joints in planarmultibody systems, Nonlinear Dyn. 70 (2012) 2145-2161.
[19] M. Langerholc, M. Cesnik, J. Slavic, M. Boltear, Experimental validation of a complex, large scale, rigid-body mechanism, Eng. Struct. 36 (2012) 220-227.
[20] X.M. Bai, B. Shah, L.M. Keer, Q.J. Wang, R.Q. Snurr, Particle dynamics simulations of piston-based paricle damper, Powder Technol. 189 (2009) 115-125.
[21] Z. Lu, X. Lu, S.F. Masri, Studies of the performance of particle dampers under dynamic loads, J. Sound. Vib. 329 (2010) 5415-5433.
[22] D.Q. Wang, C.J. Wu and R.C. Yang, Free vibration of the damping beam using co simulation method based on the MFT, Int. J. Acoust. Vib. 20 (2015) 251-257.
[23] X. Lei and C.J. Wu, Non-obstructive particle damping using principles of gas-solid flows, J. Mech. Sci. Technol. 31 (2017) 1057-1065.
[24] S. Lommen, G. Lodewijks, D.L. Schott, Co-simulation framework of discrete element method and multibody dynamics models, Eng. Computation. 35 (2018) 1481-1499.
[25] Y.C. Chung, S.S. Hsiau, H.H. Liao, J.Y. Ooi, An improved PTV technique to evaluate the velocity field of non-spherical particles, Powder technol. 202 (2010) 151-161.
[26]線性滑軌_TC，銀泰科技股份有限公司，第 B16 頁，2009。
[27] Singiresu s. Rao, Mechanical vibrations fifth edition in si units. 2011, pp. 164-166.
[28] Y.C. Chung, C.W. Wu, C.Y. Kuo, S.S. Hsiau, A rapid granular chute avalanche impinging on a small fixed obstacle: DEM modeling, experimental validation and exploration of granular stress, Appl. Math. Model. 74 (2019) 540-568.