Behavior of a Rocking Block Resting on a Rolling Isolation System

Abstract

The motion of a slender rigid block resting on an isolated base supported by rolling bearings is analyzed. This paper investigates what happens when the ground upon which the isolation system rests is subjected to a pulse-like acceleration, representative of floor motion in a building. The isolator–block system exhibits planar motion: the block may rotate about either of its bottom corners, and the isolated base may displace both horizontally and vertically. The rolling surfaces are concave and may have an arbitrary geometry, which imposes a kinematic constraint relating the base’s vertical and horizontal displacements. During an impact when the block rocks from one corner to the other, the preimpact and postimpact translational (isolator) and rotational (block) velocities are related through the principle of impulse and momentum. The response of the system is sensitive to the ground-motion parameters (amplitude and frequency), and regions of Safe (no overturning) and Unsafe (overturning) outcome are plotted in the excitation parameter plane. Boundaries between these regions are inherently sensitive to the displacement capacity of the isolation system but not to the mass ratio (block to base).