Nonlinear Impact and Chaotic Response of Slender Rocking Objects

Abstract

This investigation focuses on the influence of nonlinearities associated with impact on the behavior of the rocking response of free‐standing rigid objects subjected to horizontal base excitations. The object is to identify the causes that make the rocking response difficult to predict and that have made past experiments with identical setups and excitations unrepeatable. The impact nonlinearities examined are: (1) The transition of governing equations; and (2) the abrupt reduction in angular velocity associated with impact at the base. In addition to the periodic and overturning responses, the existence of two new types of (bounded) response not previously revealed in literature—quasi‐periodic and chaotic are discovered in this study. An approximate method based on the Melnikov function to analytically predict the existence of chaotic response is derived. Modern geometric and numerical identification techniques are employed. The accuracy of the method is assessed by numerical results. The relationship between the Melnikov analysis developed in this study and the stability analysis developed by Spanos and Koh is examined. It is shown that the divergent nature of the rocking motion in conjunction with the transition nonlinearity associated with impact constitute the major cause of the extreme sensitivity of the rocking response.