Seismic Waveguide of Metamaterials

Modern Physics Letters B (Impact Factor: 0.48). 02/2012; 26(17). DOI: 10.1142/S0217984912501059
Source: arXiv

ABSTRACT We have developed a new method of an earthquake-resistant design to support
conventional aseismic designs using acoustic metamaterials. We suggest a simple
and practical method to reduce the amplitude of a seismic wave exponentially.
Our device is an attenuator of a seismic wave. Constructing a cylindrical
shell-type waveguide that creates a stop-band for the seismic wave, we convert
the wave into an evanescent wave for some frequency range without touching the
building we want to protect.

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    ABSTRACT: In this work, we develop a general mathematical framework on regularized approximate cloaking of elastic waves governed by the Lam\'e system via the approach of transformation elastodynamics. Our study is rather comprehensive. We first provide a rigorous justification of the transformation elastodynamics. Based on the blow-up-a-point construction, elastic material tensors for a perfect cloak are derived and shown to possess singularities. In order to avoid the singular structure, we propose to regularize the blow-up-a-point construction to be the blow-up-a-small-region construction. However, it is shown that without incorporating a suitable lossy layer, the regularized construction would fail due to resonant inclusions. In order to defeat the failure of the lossless construction, a properly designed lossy layer is introduced into the regularized cloaking construction . We derive sharp asymptotic estimates in assessing the cloaking performance. The proposed cloaking scheme is capable of nearly cloaking an arbitrary content with a high accuracy.


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