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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
