Subwavelength resonances in two-dimensional high-contrast elastic media with circular inclusions

Abstract This paper employs layer potential techniques to investigate wave scattering in two-dimensional elastic media exhibiting high contrasts in both Lamé parameters and density, with the analysis restricted to circular inclusions. Our contributions are fourfold. First, we construct an invertible operator based on the kernel spaces of boundary integral operators, which enables the characterisation of resonant frequencies through an orthogonality condition. Second, we use asymptotic analysis to derive the equations governing the leading-order terms of these resonant frequencies. Third, we analyse the scattered field in the interior domain for incident frequencies across different regimes and characterise the longitudinal and transverse far-field patterns in the exterior domain. Finally, we examine the subwavelength bandgap in phononic crystals with a dilute structure.