Affiliation:
1. School of Civil Engineering, Pontifical Catholic University of Valparaiso, Brasil 2147, Level 3, Valparaiso, Valparaiso, Chile
2. School of Civil Engineering, University of Valparaiso, General Cruz 222, Level 4, Valparaiso, Valparaiso, Chile
Abstract
This technical note presents a numerical study on the stability of single degree of freedom (SDOF) systems with asymmetric bi-linear hysteretic restoring force, subjected to earthquake excitations. The aim is to report: (a) the existence of an unstable behavior in the response of such systems, under a specific ground motion, given small modifications of the yielding conditions of the hysteresis model, and (b) the introduction of a novel three-dimensional graphic visualization of the problem. The modifications of the yielding conditions were introduced via the symmetry-breaking produced by very small variations of the static equilibrium position of the system, equivalent to having an initial position and restoring force different from zero and symmetric yielding. The concise study comprises of nonlinear dynamic analyses of three system cases, one of them with symmetric (reference) and two with asymmetric yielding conditions. The results show that the system presented a stable response and severe ratcheting toward the weakest yielding direction for the symmetric and asymmetric cases, respectively. Differences as large as [Formula: see text]% between the asymmetric and reference cases were obtained for the residual displacement of the systems, due to variations as small as [Formula: see text]% in the static-equilibrium position, and consequent [Formula: see text]% variations of the positive/negative yielding displacements and forces. In turn, negligible variations of the velocity between the three cases were predicted. To conclude, the paper introduces novel three-dimensional representations of the solution-curve and of the hysteresis cycles of the systems, deepening the discussion on the identified bifurcation. The 3D hysteresis curve, in particular, can be of much use for seismic engineering and mechanical studies, either numerical or experimental, as it allows visualizing the sequence of events in the hysteresis plots in a much clearer fashion compared to the traditional two-dimensional counterparts.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Mechanical Engineering,Ocean Engineering,Aerospace Engineering,Building and Construction,Civil and Structural Engineering
Cited by
1 articles.
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