A Study on Rocking Vibration of Rigid Block Structure Accompaning Sliding Motion. In the Case of Two Dimensional Sinusodial Excitation.

Abstract

This research deals with the nonlinearities of rocking vibration which are associated with impact and sliding on the rocking behavior of rigid block under two dimensional sinusodial excitation of horizontal and vertical direction. The nonlinearities of the rocking vibration strongly depend on the impact between block and base, which should take place abrupt reduction in kinetic energy, and sliding motion which occurs during rotation and impact. Particularly, when the sliding motion occurs, the rocking behavior are massively changed by the effect of the sliding motion. The response analysis by nondimensional rocking equation is carried out for the variety of excitation level and excitation frequency. The chaotic responses are observed in the wide response region, particularly, in the case of high vertical level and small friction coefficient, and the chaotic characteristics of rocking response will be explained by the time history, Poincare map, power spectra and Lyapunov Exponent. The complex behavior of chaotic response, in the phase space, were illustrated by Poincare map. The disribution of rocking response is described as the bifurcation diagram and the effects of sliding motion are examined through the several examples of rocking response.