Criteria for Initiation of Slide, Rock, and Slide-Rock Rigid-Body Modes

The motion of a plane rigid body that rests unrestrained on a rigid foundation that is accelerating is described by five modes of response: rest, slide, rock, slide-rock, and free flight. Determining the correct initial mode of response is essential to the analysis of the generalized behavior. In the past it has been generally assumed that only a slide or rock mode can be initiated from rest. It is demonstrated in the present paper that a slide-rock mode can also be initiated from rest. Criteria governing the initiation of the slide, rock, and slide-rock modes are derived. Results show that it is incorrect to assume that a rock mode ensues if static friction is simply greater than the width-to-height ratio of the body; a slide-rock mode is initiated when friction is greater than the width-to-height ratio, but less than a critical value that is a function of the ground acceleration. The friction required to initiate a rock mode increases with ground acceleration, as would be expected. The results demonstrate a more natural transition of the governing mode of response, from sliding to slide-rock and finally to pure rocking, as friction is increased for a given foundation acceleration. The analysis is restricted to a rectangular block, assuming Coulomb friction and horizontal ground acceleration.