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dc.titleEffects of time step size on the response of a bilinear system, II: Stability analysis
dc.contributor.authorLiaw, C.Y.
dc.contributor.authorKoh, C.G.
dc.identifier.citationLiaw, C.Y.,Koh, C.G. (1991-01-08). Effects of time step size on the response of a bilinear system, II: Stability analysis. Journal of Sound and Vibration 144 (1) : 31-40. ScholarBank@NUS Repository.
dc.description.abstractThe stability of the Newmark integration method as applied to piecewise linear systems is analyzed by studying the behaviour of periodic responses on the Poincaré map. Bifurcations due to the variation of time step size are considered. Results are presented specifically for a symmetric bilinear system. An error equation is written for the Poincaré mapping in order to observe the propagation of errors due to a given initial pertubation and the numerical errors inherent in truncations and iterations. It is noted that the error propagation can be represented by the dynamics of the trace of the Jacobian matrix for the mapping. It is also observed that, even if there is no numerical error, instability due to divergence and flip bifurcations can still occur. This can lead to chaotic responses. © 1991.
dc.contributor.departmentCIVIL ENGINEERING
dc.description.sourcetitleJournal of Sound and Vibration
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