Evolution of a 3D model for free-standing rigid blocks and its behavior under base excitations

Abstract

Highly nonlinear behavior of slender rigid blocks subjected to base excitations is intended to be explored for a 3D prism. To this end, a physical model (PM) capable of handling the intricate dynamics and of viewing the motion of a rigid body during rocking/ overturning has been developed. Limited case studies show satisfactory performance of the PM to represent dynamics of such blocks both in unidirectional and bidirectional excitations. Subsequently, the dynamics of the 3D prism has been studied under trigonometric pulses. Interestingly, it appears that, under bidirectional shaking, the body may rotate about its own longitudinal axis and, due to this spin, the body may ‘walk’ from its original position even when sufficient friction at the interface prevents sliding. This residual displacement of the body under no sliding condition could not be recognized from 2D analysis. Using principles of dimensional analysis, self-similarity in response for complex nonlinear motions of the rocking oscillators has been established. This follows a comparative account on overturning spectra for 2D and 3D motions constructed in non-dimensional formats. A prognosis to chaos is uncovered from a scrutiny of long-term behavior of rocking oscillators in 3D using a set of non-dimensional parameters.