Modeling and Simulation of Rocking Block Dynamics subjected to Base Motion using an Energetic Restitution Law

This work uses a nonsmooth dynamic model to study the motion of rocking-block structures with base excitation. In this study, the rocking blocks are modeled with respect to two contact points that ...

[1]  Alan Bowling,et al.  Rebound, Slip, and Compliance in the Modeling and Analysis of Discrete Impacts in Legged Locomotion , 2006 .

[2]  Pol D. Spanos,et al.  Rocking of Rigid Blocks Due to Harmonic Shaking , 1984 .

[3]  A. Bowling,et al.  Analytic solution for planar indeterminate impact problems using an energy constraint , 2018 .

[4]  S. Hogan.  On the dynamics of rigid-block motion under harmonic forcing , 1989, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[5]  E. Dimitrakopoulos,et al.  Revisiting the rocking block: closed-form solutions and similarity laws , 2012, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[6]  Sergio Pellegrino,et al.  Free Rocking of Prismatic Blocks , 1993 .

[7]  A. Bowling,et al.  Study of Newton’s cradle using a new discrete approach , 2015 .

[8]  M. A. Serna,et al.  A modified Lagrangian formulation for the dynamic analysis of constrained mechanical systems , 1988 .

[9]  A. Bowling,et al.  Solution to indeterminate multipoint impact with frictional contact using constraints , 2012 .

[10]  J. Keller.  Impact With Friction , 1986 .

[11]  Mohammad Aslam,et al.  Earthquake Rocking Response of Rigid Bodies , 1980 .

[12]  Ioannis N. Psycharis,et al.  Complex Response of a Rocking Block to a Full-Cycle Pulse , 2014 .

[13]  Adrian Rodriguez,et al.  Dynamic simulation of multibody systems in simultaneous, indeterminate contact and impact with friction , 2014 .

[14]  E. Haug,et al.  Generalized Coordinate Partitioning for Dimension Reduction in Analysis of Constrained Dynamic Systems , 1982 .

[15]  S. Djerassi.  Stronge’s hypothesis-based solution to the planar collision-with-friction problem , 2010 .

[16]  Bernard Brogliato,et al.  Analysis of a generalized kinematic impact law for multibody-multicontact systems, with application to the planar rocking block and chains of balls , 2012 .

[17]  G. Housner.  The behavior of inverted pendulum structures during earthquakes , 1963 .

[18]  J. Penzien,et al.  Rocking response of rigid blocks to earthquakes , 1980 .

[19]  Paulo B. Lourenço,et al.  On the dynamics of rocking motion of single rigid‐block structures , 2007 .

[20]  J. Baumgarte.  Stabilization of constraints and integrals of motion in dynamical systems , 1972 .

[21]  Stefan Schaal,et al.  Inverse dynamics control of floating-base robots with external constraints: A unified view , 2011, 2011 IEEE International Conference on Robotics and Automation.

[22]  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.

[23]  William James Stronge,et al.  Smooth dynamics of oblique impact with friction , 2013 .

[24]  O. Bauchau,et al.  Review of Contemporary Approaches for Constraint Enforcement in Multibody Systems , 2008 .

[25]  Paulo B. Lourenço,et al.  Experimental Dynamic Behavior of Free-Standing Multi-Block Structures Under Seismic Loadings , 2008 .

[26]  Yildirim Hurmuzlu,et al.  Solving frictionless rocking block problem with multiple impacts , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[27]  A. Bowling,et al.  Modeling three-dimensional surface-to-surface rigid contact and impact , 2019, Multibody System Dynamics.

[28]  J. G. Jalón,et al.  Dynamic Analysis of Three-Dimensional Mechanisms in “Natural” Coordinates , 1987 .

[29]  K. Park,et al.  Stabilization of computational procedures for constrained dynamical systems , 1988 .

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

[31]  M. J. N. Priestley,et al.  SEISMIC RESPONSE OF STRUCTURES FREE TO ROCK ON THEIR FOUNDATIONS , 1978 .

[32]  Parviz E. Nikravesh,et al.  An adaptive constraint violation stabilization method for dynamic analysis of mechanical systems , 1985 .

[33]  Georg-P. Ostermeyer.  On Baumgarte Stabilization for Differential Algebraic Equations , 1990 .

[34]  S. S. Kim,et al.  QR Decomposition for State Space Representation of Constrained Mechanical Dynamic Systems , 1986 .

[35]  Bernard Brogliato,et al.  The contact problem in Lagrangian systems subject to bilateral and unilateral constraints, with or without sliding Coulomb’s friction: a tutorial , 2016, Multibody System Dynamics.

[36]  Bernard Brogliato,et al.  Dynamics of planar rocking-blocks with Coulomb friction and unilateral constraints: comparisons between experimental and numerical data , 2014 .

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

[38]  B. Koch,et al.  Heteroclinic Bifurcations and Invariant Manifolds in Rocking Block Dynamics , 1991 .