Chaotic rocking behavior of freestanding objects with sliding motion

Abstract

This paper examines the influence of effects of sliding on the non-linear rocking response behavior of freestanding rigid objects (blocks) subjected to harmonic horizontal and vertical excitations. It is well known that the rocking responses depend strongly on the impact effect between object and the base, which takes place with abrupt reduction in kinetic energy. In this study, it is shown that the rocking behavior is significantly affected by the presence of the sliding motion. A parametric response analysis is carried out over a range of excitation amplitudes and frequencies. Chaotic responses are observed over a wide response region, particularly for the case of large vertical amplitude excitation with significant sliding motions. The chaotic characteristics are demonstrated using time histories, Poincaré sections, power spectral density and Lyapunov exponents of the rocking responses. The complex chaotic response behavior is illustrated by Poincaré section in the phase space. The distribution of various types of rocking responses and the effects of sliding motion are examined via bifurcation diagrams and examples of typical rocking responses.