Chiral Seismic Attenuation with Acoustic Metamaterials

Abstract

<p class="MsoNormal" style="text-align:justify;"> <span lang="EN-US">We study the analogy between the linear elasticity theory equations and classical Maxwell equation with chiral effects and we propose 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 like an attenuator of a chiral seismic wave. Constructing a cylindrical shell-type waveguide that creates a stop-band for the chiral seismic wave, we can convert the wave into an evanescent wave for some frequency range without touching the building we want to protect.</span><span lang="EN-US"><o:p></o:p></span> </p

Parametric Instability in Mathieu Equation in Earthquake Dynamics

“…We assume that the damping coefficient is small, 0 l = εκ , and we put 2 2 0 n ω = − εβ to apply the Poincaré-Lindstedt method [9]. We find periodic solutions in the case n = 1 if: Repeating the calculations for n 2 > n ¸ 2 we find no instability domains at all; damping of O( ε ) stabilizes the system for ε small.…”

“…Force is applied in the direction that the wave is travelling; ground or earth is pretty incompressible, so the energy is transferred pretty quickly. In S wave, the medium is displaced in a transverse (up and down -compared to the line of travel) way, and the medium must shear or "move away" from the material right next to it to cause the shear and transmit the wave [1,2]. On the other hand, parametric amplifiers and oscillators have been widely studied in electronics and optics.…”

Chiral Wave Modes in Elliptical Region

“…We assume that mn m mn mn ( , ) NR ( , q ) ( , q ) Φ χ θ = χ ψ θ (14) where N is a normalization constant. After the substitution of (11) into equation (9) …”

A Seismic Channel Model: The San Ramon Fault

“…Here the electric permittivity is equivalent density of matter ε ρ → , the magnetic permeability is equivalent to the inverse of the Lamé parameter 1/ S µ µ → . The speed of transversal seismic S-waves is given by / S ρ µ [14,15] and changes of the polarization of transverse seismic waves are take into account during their propagation through the SRF.…”