Chaotic Rocking Vibration of a Rigid Block with Sliding Motion Under Two-Dimensional Harmonic Excitation

• Published in: Journal of mechanical science and technology Vol. 16; no. 9; pp. 1040 - 1053
• Main Authors: JEONG, Man-Yong, KIM, Jeong-Ho, YANG, In-Young
• Format: Journal Article
• Language: English
• Published: Seoul 대한기계학회 01.09.2002; Korean Society of Mechanical Engineers; Springer Nature B.V
• Subjects: Applied sciences; Buildings. Public works; Chaos theory; Computation methods. Tables. Charts; Exact sciences and technology; Excitation; Fundamental areas of phenomenology (including applications); Harmonic excitation; Kinetic energy; Liapunov exponents; Mathematical analysis; Nonlinearity; Physics; Poincare maps; Power spectra; Rigid blocks; Sliding; Solid dynamics (ballistics, collision, multibody system, stabilization...); Solid mechanics; Structural analysis. Stresses; Studies; Two dimensional; Vibration; Chaos; Poincaré map; Tilting; Earthquakes; Lyapunov method; Solid dynamic; Two dimensional model; Non linear effect; Modeling; Chaotic systems; Power spectrum
• ISSN: 1738-494X; 1226-4865; 1976-3824
• DOI: 10.1007/BF02984423

This research deals with the influence of nonlinearities associated with impact and sliding upon the rocking behavior of a rigid block, which is subjected to two-dimensional horizontal and vertical excitation. Nonlinearities in the vibration were found to depend strongly on the effect of the impact between the block and the base, which involves an abrupt reduction in the system's kinetic energy. In particular, when sliding occurs, the rocking behavior is substantially changed. Response analysis using a non-dimensional rocking equation was carried out for a variety of excitation levels and excitation frequencies. The chaos responses were observed over a wide response region, particularly, in the cases of high vertical displacement and violent sliding motion, and the chaos characteristics appear in the time histories, Poincare maps, power spectra and Lyapunov exponents of the rocking responses. The complex behavior of chaotic response, in phase space, is illustrated by the Poincare map. The distribution of the rocking response is described by bifurcation diagrams and the effects of sliding motion are examined through the several rocking response examples.[PUBLICATION ABSTRACT]