Rocking Response of Free-Standing Blocks under Cycloidal Pulses

Abstract

This paper examines in depth the transient rocking response of free-standing rigid blocks subjected to physically realizable trigonometric pulses. First, the expressions for the dynamic horizontal and vertical reactions at the pivot point of a rocking block are derived and it is shown that the coefficient of friction needed to sustain pure rocking motion is, in general, an increasing function of the acceleration level of the pulse. Subsequently, this paper shows that under cycloidal pulses a free-standing block can overturn with two distinct modes: (1) by exhibiting one or more impacts; and (2) without exhibiting any impact. The existence of the second mode results in a safe region that is located on the acceleration-frequency plane above the minimum overturning acceleration spectrum. The shape of this region depends on the coefficient of restitution and is sensitive to the nonlinear nature of the problem. This paper concludes that the sensitive nonlinear nature of the problem, in association with the presence of the safe region that embraces the minimum overturning acceleration spectrum, complicates further the task of estimating peak ground acceleration by only examining the geometry of free-standing objects that either overturned or survived a ground shaking.