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

## TL;DR

This paper investigates how to optimize the density distribution of non-homogeneous partially hinged plates to maximize the ratio of eigenvalues, aiding in preventing structural instability through theoretical and numerical analysis.

## Contribution

It proves the existence of optimal density functions and explores their analytic form, providing guidance for reinforcement placement in engineering applications.

## Key findings

- Existence of optimal densities is established.
- Analytic expressions for optimal densities are derived.
- Numerical experiments support theoretical results.

## 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.