Research Papers

Study of the Planar Rocking-Block Dynamics With Coulomb Friction: Critical Kinetic Angles

[+] Author and Article Information
Hongjian Zhang

State Key Laboratory for Turbulence
and Complex Systems, College of Engineering,
Peking University,
Beijing 100871, PRC
e-mail: zhanghj@pku.edu.cn

Bernard Brogliato

Senior Researcher
INRIA Grenoble Rhone-Alpes, Inovallée,
655 avenue de l'Europe, 38334 Saint-Ismier, France
e-mail: bernard.brogliato@inria.fr

Caishan Liu

ProfessorState Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, PRC e-mail: liucs@pku.edu.cn

The kinetic angle is obtained after subtraction from π because the normal vectors point outside the admissible domain of the configuration space.

The power of the potential energy ratio Eji(Pn,j,Pn,i) is inverted in Refs. [25,26].

1Work performed while at INRIA, BIPOP project-team, ZIRST Montbonnot, 655 avenue de l'Europe, 38334 Saint Ismier, France.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received March 23, 2011; final manuscript received June 21, 2012; published online July 23, 2012. Assoc. Editor: Tae-Won Park.

J. Comput. Nonlinear Dynam 8(2), 021002 (Jul 23, 2012) (11 pages) Paper No: CND-11-1042; doi: 10.1115/1.4007056 History: Received March 23, 2011; Revised June 21, 2012

The objective of this paper is to show, through the planar rocking block example, that kinetic angles play a fundamental role in multiple impact with friction. Even in the presence of Coulomb friction, a critical kinetic angle θcr is exhibited that allows one to split the blocks into two main classes: slender blocks with a kinetic angle larger than θcr, and flat blocks with a kinetic angle smaller than θcr. The value of θcr varies with the friction value, but it is independent of the restitution coefficient (normal dissipation). Numerical results are obtained using a multiple impact law recently introduced by the authors. Some comparisons between numerical and experimental results that validate the used model and numerical scheme are presented. However, this paper is mainly based on numerical simulations.

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Grahic Jump Location
Fig. 2

Admissible domain for l = 2L

Grahic Jump Location
Fig. 7

Dispersion d with μ = μs = 0, en* = 1

Grahic Jump Location
Fig. 9

θ(t) response, μ = 0.6, μs = 1, en* = 1

Grahic Jump Location
Fig. 10

Dispersion d with varying en*

Grahic Jump Location
Fig. 11

Horizontal velocity at A, μ = 0.3, μs = 0.5, en* = 1

Grahic Jump Location
Fig. 12

Dispersion d and experimental data

Grahic Jump Location
Fig. 3

The friction model

Grahic Jump Location
Fig. 4

yA(t) and yB(t), with en,1* = en,2* = 0, varying μ

Grahic Jump Location
Fig. 5

yA(t) and yB(t), with en,1* = en,2* = 0.8, varying μ

Grahic Jump Location
Fig. 6

Dispersion d with varying friction

Grahic Jump Location
Fig. 8

Stick/slip behavior at A, μ = 0.6, μs = 1, en* = 1



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