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Dynamics of planar rocking-blocks with Coulomb friction and unilateral constraints: comparisons between experimental and numerical data

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Abstract

This paper concerns the dynamics of planar rocking blocks, which are mechanical systems subject to two unilateral constraints with friction. A recently introduced multiple impact law that incorporates Coulomb friction is validated through comparisons between numerical simulations and experimental data obtained elsewhere by other authors. They concern the free-rocking motion with no base excitation, and motions with various base excitations for the study of the onset of rocking and of the overturning phenomenon. The comparisons made for free-rocking and for the onset of rocking demonstrate that the proposed impact model allows one to correctly predict the block motions. Especially the free-rocking experiments can be used to fit the impact law parameters (restitution and friction coefficients, block width). The free-rocking fitted parameters are then used in the excited-base cases.

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Notes

  1. The power of the potential energies ratio E ji (P n,j ,P n,i ) is inverted in [33, 34].

  2. All the experimental data used for the comparisons with numerical data presented in this paper have been made available to us by Dr. F. Pena from the Instituto di Ingenieria, UNAM, Mexico. They correspond to the data in the various figures and tables in [42, 43]. They can be consulted in Tables 3–8 in [63].

  3. Perfect rocking means that the block rocks without any tangential slip, and with no rebound at the impacting corners.

  4. It is important to notice here that the experiments in [43] have been led for a discrete set of amplitude values, for obvious experimental constraints. Thus, the experimentally obtained minimum amplitudes, for a given frequency, are necessarily larger than the numerical ones, which have been computed from a much finer set of amplitude values. This explains the discrepancies between the red dots and the triangles in Fig. 8(a).

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Acknowledgements

H. Zhang’s work performed while at INRIA, BIPOP project-team, ZIRST Montbonnot, 655 avenue de l’Europe, 38334 Saint Ismier, France. Funded by China Scholarship Council No. 2009601276 and by ANR project Multiple Impact ANR-08-BLAN-0321-01.

The authors are very grateful to Dr. Fernando Pena (Instituto de Ingenieria, UNAM Mexico) for providing them with detailed data from the experiments in [43]. These data have been valuable for achieving this work. This work was performed with the support of the NSFC/ANR project Multiple Impact, ANR-08-BLAN-0321-01, and with support of the NSFC key project (Grant No. 11132001).

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  1. State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing, 100871, People’s Republic of China

    Hongjian Zhang & Caishan Liu

  2. INRIA, BIPOP project-team, ZIRST Montbonnot, 655 avenue de l’Europe, 38334, Saint Ismier, France

    Bernard Brogliato

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  1. Hongjian Zhang
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Correspondence to Bernard Brogliato.

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Zhang, H., Brogliato, B. & Liu, C. Dynamics of planar rocking-blocks with Coulomb friction and unilateral constraints: comparisons between experimental and numerical data. Multibody Syst Dyn 32, 1–25 (2014). https://doi.org/10.1007/s11044-013-9356-9

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