Quarterly of Applied Mathematics

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Stability of negative stiffness viscoelastic systems

Author(s): Yun-Che Wang; Roderic Lakes
Journal: Quart. Appl. Math. 63 (2005), 34-55.
MSC (2000): Primary 74B10; Secondary 74C10, 74D05
Posted: December 17, 2004
MathSciNet review: 2126568
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: We analytically investigate the stability of a discrete viscoelastic system with negative stiffness elements both in the time and frequency domains. Parametric analysis was performed by tuning both the amount of negative stiffness in a standard linear solid and driving frequency. Stability conditions were derived from the analytical solutions of the differential governing equations and the Lyapunov stability theorem. High frequency response of the system is studied. Stability of singularities in the dissipation $\tan \delta$ is discussed. It was found that stable singular $\tan \delta$ is achievable. The system with extreme high stiffness analyzed here was metastable. We established an explicit link for the divergent rates of the metastable system between the solutions of differential governing equations in the time domain and the Lyapunov theorem.

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