Analytical modeling of damped locally-resonant metamaterials

IF 2.1 3区 物理与天体物理 Q2 ACOUSTICS
Sabiju Valiya Valappil , Alejandro M. Aragón
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引用次数: 0

Abstract

Locally-resonant metamaterials (LRMMs) are architected materials that can be designed to manipulate mechanical wave propagation by tuning their band gaps. Discrete lumped-mass models and discrete distributed-mass finite element models are both generally used to analyze LRMMs. While the former is accurate only near the fundamental resonance frequency of resonators, the latter’s accuracy is tightly coupled to the computational cost. In this study, an analytical procedure based on the spectral element method (SEM) is proposed to analyze both undamped and damped LRMMs as continuous systems. We compare LRMMs’ band structures to those obtained by discrete models and show that the proposed procedure is capable of capturing the wave dynamics of these materials very accurately and with negligible computational cost. The behavior of a finite LRMM waveguide is also studied through displacement transmissibility. In addition to the attenuation provided by band gaps, we investigate the effects of constant viscous damping and frequency-dependent viscoelastic damping, which proved to be a straightforward extension of the undamped spectral element model.
阻尼局部共振超材料的解析建模
局部共振超材料(LRMMs)是一种可以通过调节其带隙来操纵机械波传播的结构材料。离散集中质量模型和离散分布质量有限元模型都是分析lrmm的常用方法。前者仅在谐振器的基频附近精确,而后者的精度与计算成本紧密耦合。在本研究中,提出了一种基于谱元法(SEM)的分析方法,将无阻尼和有阻尼的lrmm作为连续系统进行分析。我们将LRMMs的能带结构与离散模型获得的能带结构进行了比较,并表明所提出的程序能够非常准确地捕获这些材料的波动动力学,并且计算成本可以忽略不计。通过位移透射率研究了有限LRMM波导的特性。除了带隙提供的衰减外,我们还研究了恒定粘性阻尼和频率相关粘弹性阻尼的影响,这被证明是无阻尼谱单元模型的直接扩展。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Wave Motion
Wave Motion 物理-力学
CiteScore
4.10
自引率
8.30%
发文量
118
审稿时长
3 months
期刊介绍: Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics. The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.
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