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Indexed by:期刊论文

Date of Publication:2009-03-01

Journal:SOIL DYNAMICS AND EARTHQUAKE ENGINEERING

Included Journals:SCIE、EI、Scopus

Volume:29

Issue:3

Page Number:459-468

ISSN No.:0267-7261

Key Words:Capacity spectrum method; Convergence; Chaotic dynamics; Periodic oscillation and chaos; Lyapunov exponent; Chaos control; Stability transformation

Abstract:The capacity spectrum method (CSM), capable of predicting the demands of forces and deformations of the inelastic system, has been applied in the ATC and FEMA guidelines. The deformation of an inelastic system is solved iteratively by using the equivalent linearization for CSM, which actually forms a nonlinear map or discrete dynamical system. However, the iterative procedure of CSM did not converge for some inelastic systems, and the complicated dynamical phenomena for the solutions such as the periodic oscillation, period-doubling bifurcation and chaos may occur, which were shown in the bifurcation plots of iterative map of the simplified CSM in ATC40 and FEMA440. This paper presents a novel method to analyze and control the non-convergence of the iterative procedure of CSM from the perspective of chaotic dynamics. The Lyapunov exponent of the dynamical system is employed to identify the evolutional state and stability of solutions. Finally, the stability transformation method as a simple. versatile and effective chaos feedback control approach is applied to control the convergent failure of CSM in ATC40 and FEMA440. The numerical results illustrate that the stability transformation method call capture the desired fixed points of the dynamical system and obtain the stable convergent solutions of CSM. (C) 2008 Elsevier Ltd. All rights reserved.