Construction of exceptional points in time-modulated high-contrast elastic media

This work investigates the subwavelength spectral properties of high-contrast elastic metamaterials in Rd (d ≥ 2), comprising periodic arrays of rigid inclusions embedded within a compliant matrix. We present three principal contributions. First, we establish the asymptotic behavior of subwavelength resonant frequencies for static configurations, deriving their explicit dependence on the contrast parameter, thereby determining the subwavelength frequency range. Second, for time-modulated structures, we obtain a finite-dimensional system of ordinary differential equations (ODEs) governing the subwavelength dynamics and prove that this reduced model faithfully captures the resonant quasi-frequency behavior of the original system. Finally, by combining this ODE reduction with Floquet theory, we construct the first rigorous examples of first-order asymptotic exceptional points in three-dimensional elastic media.