Chaos on the Rocking Vibration of Rigid Block Under Two Dimensional Sinusodial Excitation (In the Case of No Sliding Occurrence)

2차원 정현파 가진을 받는 강체블록의 록킹진동에 있어서의 카오스 (미끄럼이 없는 경우에 대하여)

This research deals with the non-linearities associated with impact and sliding for the rocking behavior of rigid block subjected to two dimensional excitation of horizontal and vertical direction. The non-linearities examined of impact between block and base: The transition of two governing rocking equations, the abrupt reduction in kinetic energy associated with impact. In this study, the rocking vibration system of two types are considered for several friction condition. One is the undamped rocking vibration system, disregarding energy dissipation at impact and the other is the damped rocking system, including energy dissipation at impact. The response analysis by non-dimensional rocking equation is carried out for the change of excitation amplitude. The chaos responses were discovered in the wide response region, particularly, in the case of high vertical excitation and their chaos characteristics are examined by Poincare map, power spectra and Lyapunov Exponent. The complex behavior of chaos response, in the phase space, were illustrated by Poincare map. Therefore, Poincare map will be a significant material in order to understand chaos of rocking system.