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    Study of a piecewise linear dynamic system with negative and positive stiffness

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    Author
    Zou, Keguan; Nagarajaiah, Satish
    Date
    2014
    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.
    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.
    Published Version
    http://dx.doi.org/10.1016/j.cnsns.2014.08.016
    Keyword
    piecewise smooth system; negative stiffness; modified Lindstedt–Poincaré method; analytical approximation
    Type
    Journal article
    Publisher
    Elsevier
    Citable link to this page
    https://hdl.handle.net/1911/77437
    Rights
    This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier.
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    Home | FAQ | Contact Us | Privacy Notice | Accessibility Statement
    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
    Mailing Address: MS-44, P.O.BOX 1892, Houston, Texas 77251-1892
    Site Map