Maximizing the ratio of eigenvalues of non-homogeneous partially hinged plates
Analysis of PDEs
2020-08-31 v2 Spectral Theory
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.
Keywords
Cite
@article{arxiv.1907.11097,
title = {Maximizing the ratio of eigenvalues of non-homogeneous partially hinged plates},
author = {Elvise Berchio and Alessio Falocchi},
journal= {arXiv preprint arXiv:1907.11097},
year = {2020}
}