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

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