Maximizing the ratio of eigenvalues of non-homogeneous partially hinged plates

  • Elvise Berchio

    Polytechnic University of Turin, Italy
  • Alessio Falocchi

    Polytechnic University of Turin, Italy
Maximizing the ratio of eigenvalues of non-homogeneous partially hinged plates cover
Download PDF

This article is published open access under our Subscribe to Open model.

Abstract

We study the spectrum of non-homogeneous partially hinged plates having structural engineering applications. A possible way to prevent instability phenomena is to maximize the ratio between the frequencies of certain oscillating modes with respect to the density function of the plate; we prove existence of optimal densities and we investigate their analytic expression. This analysis suggests where to locate reinforcing material within the plate; some numerical experiments give further information and support the theoretical results.

Cite this article

Elvise Berchio, Alessio Falocchi, Maximizing the ratio of eigenvalues of non-homogeneous partially hinged plates. J. Spectr. Theory 11 (2021), no. 2, pp. 743–780

DOI 10.4171/JST/355