Rebound of a confined granular material: combination of a bouncing ball and a granular damper

A ball dropped over a solid surface bounces several times before a complete stop. The bouncing can be reduced by introducing a liquid into the ball; however, the first rebound remains largely unaffected by the fluid. Granular materials can also work as dampers. We investigated the rebound of a container partially filled with a given mass of grains mi. During the collision, the kinetic energy of the container is partially transferred to the grains, the rebound is damped, and the fast energy dissipation through inter-particle collisions and friction decreases the bouncing time dramatically. For grain-filled cylinders, a completely inelastic collision (zero rebound) is obtained when mi ≥ 1.5εomc, where εo and mc are the coefficient of restitution and mass of the empty container. For grain-filled spheres, the first rebound is almost undamped, but the second collision is completely inelastic if mi ≫ mc. These findings are potentially useful to design new granular damping systems.

[1]  P. Umbanhowar,et al.  Localized excitations in a vertically vibrated granular layer , 1996, Nature.

[2]  Hagop V. Panossian,et al.  Structural Damping Enhancement Via Non-Obstructive Particle Damping Technique , 1992 .

[3]  George Barnes,et al.  Study of Collisions. Part. I. A Survey of the Periodical Literature , 1958 .

[4]  Kuanmin Mao,et al.  Simulation and Characterization of Particle Damping in Transient Vibrations , 2004 .

[5]  M. N. Bannerman,et al.  Movers and shakers: granular damping in microgravity. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  N. Vandewalle,et al.  Phase transitions in vibrated granular systems in microgravity. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  J. C. Ruiz-Suárez,et al.  Superheating in granular matter. , 2009, Physical review letters.

[8]  B. Brogliato,et al.  Planar dynamics of a rigid body system with frictional impacts. II. Qualitative analysis and numerical simulations , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[9]  Taichi Sato,et al.  Vibration isolation in a system using granular medium , 1995 .

[10]  T. Schwager,et al.  Coefficient of restitution of colliding viscoelastic spheres. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  Steven Ashley.  A new spin on the rotary engine , 1995 .

[12]  Steve Haake,et al.  Impact of a non-homogeneous sphere on a rigid surface , 2004 .

[13]  Philippe Gondret,et al.  Bouncing motion of spherical particles in fluids , 2002 .

[14]  Cross,et al.  Dynamic properties of tennis balls , 1999 .

[15]  Leon M Keer,et al.  Investigation of particle damping mechanism via particle dynamics simulations , 2009 .

[16]  Luis A. Pugnaloni,et al.  Effective mass overshoot in single degree of freedom mechanical systems with a particle damper , 2011, 1105.0304.

[17]  Clara Saluena,et al.  DISSIPATIVE PROPERTIES OF VIBRATED GRANULAR MATERIALS , 1999 .

[18]  Luis A. Pugnaloni,et al.  Universal response of optimal granular damping devices , 2012, 1201.1866.

[19]  B. Brogliato,et al.  Frictionless multiple impacts in multibody systems , 2009 .

[20]  S. Fauve,et al.  Behavior of one inelastic ball bouncing repeatedly off the ground , 1998 .

[21]  B. Brogliato,et al.  Energy dissipation and dispersion effects in granular media. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Shuguang Huang,et al.  A mass-spring-damper model of a bouncing ball , 2004, Proceedings of the 2004 American Control Conference.

[23]  Arshad Kudrolli,et al.  Cluster formation due to collisions in granular material , 1997 .

[24]  B. Brogliato,et al.  Frictionless multiple impacts in multibody systems. I. Theoretical framework , 2008 .

[25]  Mehta,et al.  Novel temporal behavior of a nonlinear dynamical system: The completely inelastic bouncing ball. , 1990, Physical review letters.

[26]  Thorsten Pöschel,et al.  Granular dampers for the reduction of vibrations of an oscillatory saw , 2012 .

[27]  Clément,et al.  Studies of columns of beads under external vibrations. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[28]  Michael Yu Wang,et al.  Dissipation mechanisms of nonobstructive particle damping using discrete element method , 2001, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[29]  Benjamin F Bayman,et al.  Model of the behavior of solid objects during collision , 1976 .

[30]  P. Gray.  The Completely Inelastic Bouncing Ball , 2011 .

[31]  Zhen Zhao,et al.  Variable structure dynamics in a bouncing dimer , 2008 .

[32]  Panayiotis Papadopoulos,et al.  Dynamics of pseudo-rigid ball impact on rigid foundation , 2004 .

[33]  B. Bernu,et al.  One-dimensional bounce of inelastically colliding marbles on a wall , 1990 .

[34]  N. Vandewalle,et al.  Bouncing trimer: a random self-propelled particle, chaos and periodical motions , 2008, 0808.2936.

[35]  S. Ashley,et al.  A new racket shakes up tennis , 1995 .

[36]  D Volfson,et al.  Dynamics of a bouncing dimer. , 2005, Physical review letters.

[37]  B. Brogliato,et al.  Frictionless multiple impacts in multibody systems. II. Numerical algorithm and simulation results , 2008, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[38]  Taylor W. Killian,et al.  Rebound and jet formation of a fluid-filled sphere , 2012 .

[39]  R. Cross.  The bounce of a ball , 1999 .