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Title: Effects of time step size on the response of a bilinear system, II: Stability analysis
Authors: Liaw, C.Y. 
Koh, C.G. 
Issue Date: 8-Jan-1991
Citation: Liaw, 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.
Abstract: The 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.
Source Title: Journal of Sound and Vibration
ISSN: 0022460X
Appears in Collections:Staff Publications

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