Estimates for sums of eigenvalues of the free plate with nonzero Poisson's ratio

TL;DR

This paper derives bounds for sums of eigenvalues of the free plate with nonzero Poisson's ratio using Fourier transform techniques, relating these bounds to domain and material properties.

Contribution

It provides Kröger-type estimates for eigenvalue sums of the free plate considering tension and nonzero Poisson's ratio, extending previous spectral bounds.

Findings

Established eigenvalue sum bounds depending on domain volume and material parameters.

Extended spectral estimates to plates with nonzero Poisson's ratio.

Applied Fourier transform to derive explicit eigenvalue inequalities.

Abstract

By using the Fourier transform, we successfully give Kr\"{o}ger-type estimates for sums of eigenvalues of the free plate (under tension and with nonzero Poisson's ratio) in terms of the dimension of the ambient space, the volume of the domain, the tension parameter and the Poisson's ratio.