Nonlinear Dynamics of a Rigid Block on a Rigid Base

[+] Author and Article Information
R. N. Iyengar, D. Roy

Department of Civil Engineering, Indian Institute of Science, Bangalore 560 012, India

J. Appl. Mech 63(1), 55-61 (Mar 01, 1996) (7 pages) doi:10.1115/1.2787209 History: Received January 24, 1994; Revised December 08, 1994; Online October 26, 2007


The planar rocking of a prismatic rectangular rigid block about either of its corners is considered. The problem of homoclinic intersections of the stable and unstable manifolds of the perturbed separatrix is addressed to and the corresponding Melnikov functions are derived. Inclusion of the vertical forcing in the Hamiltonian permits the construction of a three-dimensional separatrix. The corresponding modified Melnikov function of Wiggins for homoclinic intersections is derived. Further, the 1-period symmetric orbits are predicted analytically using the method of averaging and compared with the simulation results. The stability boundary for such orbits is also established.

Copyright © 1996 by The American Society of Mechanical Engineers
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