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Mathematical modeling and analysis of a meta-plate for very low-frequency band gap

机译：极低频带隙的Meta-plate的数学建模和分析

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摘要

Aiming to attenuate very low-frequency flexural wave in a thin plate, this paper proposes a meta-plate model by periodically attaching high-static-low-dynamic-stiffness (HSLDS) resonators onto the thin plate. The HSLDS resonator consists of a linear spring with a negative stiffness mechanism (NSM) in parallel, and thus its stiffness can be adjusted to any low values within a range from zero to the stiffness of the linear spring. Using the plane-wave expansion (PWE) method, and considering the linearized stiffness of the resonator, the dispersion relation of the meta-plate can be derived and the band structure can be obtained. A dynamic model of the meta-plate with the original nonlinear stiffness under external excitations is also established. The numerical simulations are carried out by the Galerkin method to evaluate the band structure and study the propagation of the flexural wave along the meta-plate with different azimuth angles. The analytical results exhibit good agreement with the numerical ones, which indicates that the proposed meta-plate can create a very low-frequency band gap. (C) 2019 Elsevier Inc. All rights reserved.
机译：为了衰减薄板中的低频弯曲波，本文提出了一种通过定期在薄板上附加高静力低动态刚度（HSLDS）谐振器的元板模型。 HSLDS谐振器由线性弹簧和并联的负刚度机构（NSM）组成，因此可以将其刚度调整为从零到线性弹簧刚度的任何低值。使用平面波扩展（PWE）方法，并考虑到谐振器的线性刚度，可以推导出金属板的色散关系，并可以得到能带结构。还建立了在外部激励下具有原始非线性刚度的亚板的动力学模型。通过Galerkin方法进行了数值模拟，以评估带结构并研究挠曲波沿不同方位角的超大板的传播。分析结果与数值结果吻合良好，表明所提出的金属板可以产生很低的频带隙。 （C）2019 Elsevier Inc.保留所有权利。

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  • 来源
    《Applied Mathematical Modelling》 |2019年第9期|581-597|共17页
  • 作者

    Wang Kai; Zhou Jiaxi; Cai Changqi; Xu Daolin; Ouyang Huajiang;

  • 作者单位

    Hunan Univ, State Key Lab Adv Design & Mfg Vehicle Body, Changsha 410082, Hunan, Peoples R China|Hunan Univ, Coll Mech & Vehicle Engn, Changsha 410082, Hunan, Peoples R China;

    Hunan Univ, State Key Lab Adv Design & Mfg Vehicle Body, Changsha 410082, Hunan, Peoples R China|Hunan Univ, Coll Mech & Vehicle Engn, Changsha 410082, Hunan, Peoples R China;

    Hunan Univ, State Key Lab Adv Design & Mfg Vehicle Body, Changsha 410082, Hunan, Peoples R China|Hunan Univ, Coll Mech & Vehicle Engn, Changsha 410082, Hunan, Peoples R China;

    Hunan Univ, State Key Lab Adv Design & Mfg Vehicle Body, Changsha 410082, Hunan, Peoples R China|Hunan Univ, Coll Mech & Vehicle Engn, Changsha 410082, Hunan, Peoples R China;

    Univ Liverpool, Sch Engn, Liverpool L69 3GH, Merseyside, England;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    High-static-low-dynamic-stiffness resonator; Meta-plate; Very low frequency band gap; Plane-wave expansion method;

    机译：高静低动力刚度谐振器;金属板;极低的频带隙;平面波扩展法;

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