Chaos on Rocking Vibration of Rigid Block Structure under Two Dimensional Sinusodial Excitation. For the Case of No Sliding.

Abstract

This research concentrates on the influence of nonlinearities associated with impact for the rocking behavior of rigid block subjected to two dimensional excitation of horizontal and vertical. The nonlinearities in the vibration strongly depend on the impact effect between block and base which should take place abrupt reduction in kinetic energy. In this study, the rocking vibration system of two types are considered. One is the undamped rocking vibration system by disregarding energy dissipation at impact and another is the damped rocking system, including energy dissipation at impact. The response analysis by nondimensional rocking equation is carried out for the variety of excitation level. The chaos responses can be observed in the wide response region, particularly, for the case of high vertical level and the chaos characteristics appear in the time histories, Poincare maps, power spectra and Lyapunov Exponents of rocking responses. The complex behavior of chaos response, in the phase space, were illustrated by Poincare map.