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<doi>GS-03-060-cd</doi>

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<article-title>Probability distribution of vibration isolation area in phonon crystal arrays with finite length </article-title>
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<author>Xiaolei Li<sup>1</sup>, Xuhong Zhou<sup>1,2</sup>, and Yongtao Bai<sup>1,2</sup></author>

<aff><sup>1</sup>School of Civil Engineering, Chongqing University, China</aff>

<aff><sup>2</sup>Research Center for Steel Structure Engineering, Chongqing University, China </aff>

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<title>ABSTRACT</title>
<p>The bandgap characteristics of a one-dimensional phonon crystal array can suppress the propagation of seismic waves and reduce the risk of extreme vibration triggered by earthquake ground motions. To find the impact of the finite size of the phonon crystal array on the vibration isolation efficiency under seismic excitations, the bandgap of the one-dimensional phonon crystal is first obtained through the analytical solution. Then we simulate the wave field of a finite-size strip phonon crystal array on a two-dimensional plane by the method of finite differ in time domain (FDTD). The results show that the input wave to the phonon crystal array is mainly reflected instead of being absorbed, which results in a response-enhanced area at the front of the array and an attenuation area on the filtered back. For obtaining the probability characteristics of amplification and attenuation effects, a small sample considering the uncertainty of material properties and length is obtained by Latin Hypercube Sampling (LHS). Probability distributions for the associated amplification and attenuation coefficients are obtained to be normal distribution with reasonable tolerance of engineering error.</p><p> <italic>Keywords:</italic>Seismic Metamaterial, Vibration Isolation, Phonon Crystal, Latin Hypercube Sampling, Bandgap Frequency </p></abstract>
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