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dc.contributor.authorZou, Keguan
Nagarajaiah, Satish
dc.date.accessioned 2014-10-07T23:23:50Z
dc.date.available 2014-10-07T23:23:50Z
dc.date.issued 2014
dc.identifier.citation Zou, Keguan and Nagarajaiah, Satish. "Study of a piecewise linear dynamic system with negative and positive stiffness." Communications in Nonlinear Science and Numerical Simulation, (2014) Elsevier: http://dx.doi.org/10.1016/j.cnsns.2014.08.016.
dc.identifier.urihttps://hdl.handle.net/1911/77437
dc.description.abstract The present paper mainly focuses on numerical and analytical study of a piecewise linear dynamic oscillator with negative stiffness followed by positive stiffness which has not been studied to date. The dynamic system of interest stems from a previous analytical and experimental research on adaptive negative stiffness for the purpose of seismic protection. Numerical algorithms meant specifically for simulating piecewise smooth (PWS) systems like this nonlinear system are studied. An appropriate combination of negative stiffness and adequate damping can reduce the peak restoring or transmitted force with a slightly larger peak displacement. Essentially, the negative stiffness system in a dynamic system is very beneficial in reducing the amount of force transmitted. The exact solution is derived for free vibration. A modified Lindstedt–Poincaré method (modified L–P method) is adopted to derive approximate periodic solutions for the forced and damped system and its frequency-response curves are obtained through numerical simulation. The modified L–P solution obtained for the forced and damped case is found to agree well with the numerical results. In the piecewise linear dynamic system with initial negative stiffness followed by positive stiffness, it is found that the response remains bounded in a limit cycle. This system behaves similar to a van der Pol oscillator wherein negative damping is followed by positive damping. Presented herein is a special case as defined by the specified parameter ranges; thus, to make it more general future work is needed.
dc.language.iso eng
dc.publisher Elsevier
dc.rights This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier.
dc.title Study of a piecewise linear dynamic system with negative and positive stiffness
dc.type Journal article
dc.contributor.funder China Scholarship Council
dc.citation.journalTitle Communications in Nonlinear Science and Numerical Simulation
dc.subject.keywordpiecewise smooth system
negative stiffness
modified Lindstedt–Poincaré method
analytical approximation
dc.type.dcmi Text
dc.identifier.doihttp://dx.doi.org/10.1016/j.cnsns.2014.08.016
dc.type.publication post-print


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