Nonlinear rigid block dynamics

Abstract

Motion of a block on flat ground under the influence of gravity is studied. A general model is introduced for the free motion of a rectangular, rigid block on a continuous, perfectly elastic foundation. The model includes friction forces between the block and foundation and allows for sliding, rocking and flight of the block. Solutions are obtained through numerical integration. A three parameter study is carried out, namely as a function of aspect ratio, r, coefficient of friction, ì, and non-dimensional stiffness, k_, for various initial conditions. Dominant types of response are identified and the stability of the block again overturning and its tendency to fly are studied. For initial conditions with sufficient energy, critical curves are found in the (k-, r) parameter space which define a transition between a flight and no flight region. For initial conditions with sufficient energy there also exists a critical curve in the same parameter space which separates a region of overturning from a region where the block does not overturn. Chaos is found in the flight region of the (k_, r) parameter space for sufficiently high r. Poincare maps and Liapunov exponents are computed to document the existence of chaos.