Abstract
Overturning conditions for a rigid, rectangular block on a rigid, horizontal, vibrating base are investigated. The base moves with a simple-harmonic horizontal acceleration over a finite period of time, and the block can rotate about either of its bottom corners. Energy is lost during the impact when the point of rotation switches from one corner to the other. The motion of the block is investigated for various combinations of excitation amplitude and frequency. When overturning occurs, the number of prior impacts is computed. The overturning boundary in the parameter plane exhibits a fractal behavior.
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