Subwavelength resonances in two-dimensional elastic media with high contrast

Yuanchun Ren; Yixian Gao

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arXiv · 2510.01911

Subwavelength resonances in two-dimensional elastic media with high contrast

Yuanchun Ren·Yixian Gao

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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. Our contributions are fourfold. First, we construct an invertible operator based on the kernel spaces of boundary integral operators, which enables the characterization of resonant frequencies through an orthogonality condition. Second, we use asymptotic analysis to derive the equation governing the leading-order terms of these resonant frequencies. Third, we analyze the scattered field in the interior domain for incident frequencies across different regimes and characterize the longitudinal and transverse far-field patterns in the exterior domain. Finally, we examine the subwavelength bandgap in the phononic crystal with a dilute structure.

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Yuanchun Ren, Yixian Gao. 2025-10-02. Subwavelength resonances in two-dimensional elastic media with high contrast. https://arxiv.org/abs/2510.01911

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