On the first frequency of reinforced partially hinged plates

E. Berchio, A. Falocchi, ALBERTO FERRERO, D. Ganguly

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Abstract

We consider a partially hinged rectangular plate and its normal modes. The dynamical properties of the plate are influenced by the spectrum of the associated eigenvalue problem. In order to improve the stability of the plate, we place a certain amount of denser material in appropriate regions. If we look at the partial differential equation appearing in the model, this corresponds to insert a suitable weight coefficient inside the equation. A possible way to locate such regions is to study the eigenvalue problem associated to the aforementioned weighted equation. In this paper, we focus our attention essentially on the first eigenvalue and on its minimization in terms of the weight. We prove the existence of minimizing weights inside special classes and we try to describe them together with the corresponding eigenfunctions.
Lingua originaleInglese
Numero di pagine37
RivistaCommunications in Contemporary Mathematics
Numero di pubblicazione3
DOI
Stato di pubblicazionePubblicato - 2021

Keywords

  • Eigenvalues
  • plates
  • suspension bridges
  • torsional instability

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