Response of rigid bodies to base excitation

The dynamic response of unrestrained rigid bodies to base excitation is investigated. This is motivated by the need to minimize damage to essential and expensive building contents during earthquakes. Behavior is studied for a rectangular block, considering all five modes of response: rest, slide, rock, slide-rock and free-flight. Impact is considered from a rock, slide-rock or free-flight mode using relations which are derived from first principles. Vertical ground acceleration is neglected.;The method of slowly varying parameters is used to develop an approximate closed-form solution for a steady-state slide-rock response resulting from a harmonic ground acceleration. Solutions in general exist only for relatively high amplitudes of ground acceleration. The rock component of the response is sensitive to changes in aspect ratio and friction, and insensitive to changes in ground acceleration: the opposite is true for the slide component. Results compare favorably to those obtained by numerical integration.;A modified slowly varying parameter solution is developed for nonlinear systems subject to periodic loads which are impulsive in nature (e.g., rock or slide-rock). The proposed solution admits a discontinuity in velocity that is produced by the impulsive load. Examples are given which demonstrate the improvement in accuracy of the proposed solution.;A program is described which has been developed to compute the response numerically. Application of the program is demonstrated for a range of system parameters and three forms of ground acceleration: initial-value problems and the response to harmonic and recorded earthquake ground motion.;Previous investigations to consider this behavior have generally been restricted to a single mode response: slide or rock. The validity of the assumptions made in these analyses are examined. Free and steady-state rocking solutions are shown to be generally valid for relatively tall blocks and a range of friction and restitution parameters. Slide solutions are shown to be valid, regardless of the form of ground acceleration, for friction less than the inverse aspect ratio. The study also demonstrates that a multiple mode response (slide and rock) due to harmonic ground motion is possible under certain conditions.