An isoperimetric inequality for fundamental tones of free plates with nonzero Poisson's ratio

TL;DR

This paper extends an isoperimetric inequality to the fundamental tone of free plates with nonzero Poisson's ratio, broadening the understanding of eigenvalue bounds in elastic plate theory.

Contribution

It provides a partial generalization of a known inequality to plates with nonzero Poisson's ratio, which was not previously established.

Findings

Extended the isoperimetric inequality to nonzero Poisson's ratio plates

Established bounds for the fundamental tone in this new setting

Contributed to the mathematical understanding of elastic plate vibrations

Abstract

We establish a partial generalization of a prior isoperimetric inequality for the fundamental tone (first nonzero eigenvalue) of the free plate to plates of nonzero Poisson's ratio.