Spectral patterns of elastic transmission eigenfunctions: boundary localisation, surface resonance and stress concentration

TL;DR

This paper investigates the spectral patterns of elastic transmission eigenfunctions, revealing boundary localisation, surface resonance, and stress concentration, supported by rigorous analysis and numerical verification across various geometries.

Contribution

It provides the first comprehensive analysis of spectral patterns in elastic transmission eigenfunctions, including rigorous justifications and numerical validation beyond radial domains.

Findings

Boundary localisation of eigenfunctions

Surface resonance phenomena

Stress concentration patterns

Abstract

We present a comprehensive study of new discoveries on the spectral patterns of elastic transmission eigenfunctions, including boundary localisation, surface resonance, and stress concentration. In the case where the domain is radial and the underlying parameters are constant, we give rigorous justifications and derive a thorough understanding of those intriguing geometric and physical patterns. We also present numerical examples to verify that the same results hold in general geometric and parameter setups.