Stability of negative stiffness viscoelastic systems

Yun Che Wang, Roderic Lakes

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)

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 δ is discussed. It was found that stable singular tan δ 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.

Original languageEnglish
Pages (from-to)34-55
Number of pages22
JournalQuarterly of Applied Mathematics
Volume63
Issue number1
DOIs
Publication statusPublished - 2005 Mar

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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