Frictional Aspect of Rocking-Sliding of a Rigid Block with Surface Impact

by Majid Shekarian, Rice Univ, Houston, United States,
Joel P. Conte, Rice Univ, Houston, United States,
Pol D. Spanos, Rice Univ, Houston, United States,

Abstract: During the very short time of impact between a rigid rectangular block and a rigid foundation, the interface pressure distribution varies with time in a complicated manner. Due to this spatially distributed impulse, the block may either rotate or rotate and slide simultaneously. In this paper, a linear prssure distribution is assumed, starting from zero at the 'rotating' corner and ending with a maximum value at the 'hitting' corner. The ratio of the angular velocities before and after impact, commonly called coefficient of restitution, is derived in terms of the material coefficient of friction and the aspect ratio of the block. The friction between block and foundation is modeled as Coulomb friction characterized by the coefficient of friction. The derived results show that for a given aspect ratio of the block, a minimum value for the coefficient of friction is required to prevent sliding after impact. Conversely, for a prescribed coefficient of friction, a minimum aspect ratio is necessary to keep the block in a pure rocking mode.

Subject Headings: Friction | Pressure distribution | Foundations | Rotation | Dynamic pressure | Spatial distribution | Sliding effects | Equations of motion

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