FRACTAL BEHAVIOR OF AN ASYMMETRIC RIGID BLOCK OVERTURNING DUE TO HARMONIC MOTION OF A TILTED FOUNDATION

The motion of a slender rigid block with a flat or concave base restin g on a rigid and flat foundation is analyzed. The block may be symmetr ic or asymmetric, and the foundation may be horizontal or tilted. The foundation oscillates harmonically for a finite period of time, and th e block exhibits planar motion: it may rotate about either of its bott om corners, it may rock from one corner to the other, and it may overt urn. Sliding and bouncing are not considered. Energy is lost during th e impact when the point of rotation switches from one corner to the ot her. The number of impacts prior to overturning is computed, and resul ts for horizontal foundation acceleration are plotted in the plane of excitation amplitude versus excitation frequency. The boundaries separ ating regions associated with different numbers of impacts, and in par ticular the boundary between overturning and nonoverturning regions, a re fractal.