Research article Special Issues

Beams with an intermediate pier: Spectral properties, asymmetry and stability

  • This contribution is part of the Special Issue: Qualitative Analysis and Spectral Theory for Partial Differential Equations
    Guest Editor: Veronica Felli
    Link: www.aimspress.com/mine/article/5511/special-articles
  • Received: 16 March 2020 Accepted: 28 May 2020 Published: 29 June 2020
  • We deal with beams with an intermediate pier, motivated by the investigation of the stability of suspension bridges with two spans. First, we provide a complete spectral theorem for the associated linear stationary fourth-order problem with hinged boundary conditions, determining the eigenvalues and discussing their optimality (in a suitable sense) in terms of the position of the pier. Then, we consider a related nonlinear model with a restoring force of superquadratic displacement type, discussing its stability both from a linear and from a suitable nonlinear point of view. We determine the position of the pier maximizing the stability of the structure and we compare the energy thresholds of instability under hinged, clamped or mixed (left-clamped and right-hinged) boundary conditions. In any case, we highlight that an asymmetric structure is in general more stable.

    Citation: Maurizio Garrione. Beams with an intermediate pier: Spectral properties, asymmetry and stability[J]. Mathematics in Engineering, 2021, 3(2): 1-21. doi: 10.3934/mine.2021016

    Related Papers:

  • We deal with beams with an intermediate pier, motivated by the investigation of the stability of suspension bridges with two spans. First, we provide a complete spectral theorem for the associated linear stationary fourth-order problem with hinged boundary conditions, determining the eigenvalues and discussing their optimality (in a suitable sense) in terms of the position of the pier. Then, we consider a related nonlinear model with a restoring force of superquadratic displacement type, discussing its stability both from a linear and from a suitable nonlinear point of view. We determine the position of the pier maximizing the stability of the structure and we compare the energy thresholds of instability under hinged, clamped or mixed (left-clamped and right-hinged) boundary conditions. In any case, we highlight that an asymmetric structure is in general more stable.


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