多孔压电分流超材料及其带隙特性研究

设计了一种新型多孔压电分流超材料构型,以单、双孔元胞构型为例,研究了其带隙特性和有限周期振动传递特性,并与未开孔压电分流超材料板进行了对比分析。计算结果表明:与未开孔压电超材料相比,两种构型在低频处的压电局域共振带隙频率更低,带宽变窄,且均会在高频范围内出现额外带隙,随着孔宽δ的增大,额外带隙数量逐渐增多;对应特定的孔宽δ的两种元胞构型均产生带宽大于1kHz的超宽带隙。该构型结合了压电分流超材料和声子晶体的特点,与传统未开孔压电分流超材料相比,具备低频和高频同时抑振的特性。     

力-压电混合弹性超材料梁的带隙调节特性

为实现宽带低频减振,本文将力振子和串联负电容的压电分流振子分别置于基体上下两侧,设计了混合弹性超材料梁。基于传递矩阵法建立了理论模型,用于计算混合弹性超材料梁的频散关系和动态有效参数,通过有限元法进行了验证。分别采用理论方法和数值方法研究了电路元件参数对混合弹性超材料梁的带隙和振动衰减特性的调节机理,通过与单振子超材料的带隙对比,分析了两种振子间的相互影响。结果表明：电路元件参数主要影响压电分流振子产生的带隙的位置、宽度及带隙内的振动衰减程度;两种振子的带隙重叠区域不一定为通带;两种振子会因为负动态有效刚度范围靠近而相互影响。本研究将为此类超材料的设计提供参考依据。     

圆管型局域共振声子晶体三维构型振动带隙研究

采用多重多级子结构方法计算具有一定刚度的圆管型局域共振声子晶体三维构型振动带隙特性。考察包裹方向对带隙特性的影响,并对第一带隙上下边界点的单胞振动形式进行分析。结果表明,两种包裹形式都可以得到较低较宽的第一带隙,并且带隙特性相似,因而其周期结构都可以大幅减弱带隙范围内弹性波的传播。但两种构型带隙上下边界点对应振动形式不同,此外带隙特性还受单胞尺寸的影响。通过给定评价指标得到相关材料参数与带隙特性关系的相图,由此分析包裹层材料属性对带隙特性的影响。     

低频振动隔离和能量采集双功能超材料

振动隔离和能量采集一体化是一种能够将有害振动隔离并转化为电能收集利用的动力学机制. 本文从局域共振超材料存在低频带隙特性出发, 研究了振动隔离和能量采集双功能超材料的动力学行为. 通过在球型磁腔内放置固接了感应线圈的球摆构成具有能量采集功能的球摆型谐振器, 并将其周期性的放置在基体梁中, 可以将带隙频率范围内的振动聚集在谐振器内, 以实现振动隔离和能量采集双功能. 建立了横向激励下双功能超材料梁的动力学方程, 应用Bloch's定理得到超材料的能带结构, 通过有限元仿真验证了理论模型和研究方法. 研究了不同参数下超材料梁的带隙特性. 进一步将一维拓展到二维, 研究了二维双功能超材料板的振动隔离和能量采集性能. 最后, 设计并建造了振动隔离和能量采集一体化双功能超材料动力学实验平台, 解析、数值和实验结果表明, 在局域共振带隙的频率范围内, 超材料梁主体的振动明显被抑制, 与此同时, 振动被局限在谐振器中, 使采集到的电压达到了最大值. 通过对附加谐振器和没有附加谐振器的能带结构和幅频响应的对比, 发现球摆型谐振器的加入可以在低频范围内形成了一个局域共振带隙, 有效提高了超材料梁在低频处的振动隔离和能量采集性能.      

超材料混凝土的带隙特征及对冲击波的衰减效应

借鉴超材料的研究思路，在混凝土中引入谐振骨料，设计出具有消波特性的超材料混凝土。首先，通过结构动力学方法计算超材料混凝土的有效质量，从而建立了超材料混凝土带隙起始频率及截止频率的简化模型，并给出了带隙起始频率及截止频率的理论表达式。然后，分析了涂层弹性模量、芯柱密度、基体密度、骨料体积占比和芯柱边长与软涂层厚度比对超材料混凝土带隙特征的影响。最后，采用数值模拟的方法，对比了超材料混凝土和普通混凝土对冲击波的衰减效应。研究结果表明:(1)低弹性模量涂层能够形成低频带隙，但带隙宽度较窄，而高弹性模量涂层能够形成较宽的带隙，但带隙起始频率较高；(2)通过选择高密度芯柱材料和低密度基体材料，可以得到低频、宽带隙特征；(3)通过增大骨料体积占比和芯柱边长与软涂层厚度比可以实现扩宽带隙的目的；(4)与普通混凝土相比，超材料混凝土对冲击波具有更好的衰减作用。     

周期结构后屈曲新算法及其应用

提出了周期结构后屈曲分析的一种新算法。在屈曲点附近,通过加载模型和诱导后屈曲边值问题之间的相互切换,避开屈曲点附近刚度矩阵的奇异性,并诱导结构产生预期的后屈曲变形,避免了以往后屈曲算法中引入几何初始缺陷后对系统带来的可能影响。通过对三种由超弹性材料所构成的周期孔隙结构的后屈曲分析,验证了本文所提出的后屈曲算法的有效性和灵活性。分析了周期孔隙材料多向加载对屈曲模式转换的影响,以及后屈曲变形对弹性波传播带隙的影响,为周期结构中弹性波传播的调控提供良好的基础。     

局域共振型声子晶体板缺陷态带隙及其俘能特性研究

设计了一种由圆柱形散射体嵌入环氧树脂基体而组成的周期阵列局域共振型声子晶体板结构, 分析了其平直带区域以及缺陷态的能量集中特性, 并研究了其振动能量采集特性. 首先基于超元胞法结合有限元方法分析了5 $\times$ 5完美声子晶体结构和缺陷态声子晶体结构的能带曲线和能量传输特性; 考虑点缺陷局域共振声子晶体结构的能量集中特性, 利用压电材料代替超元胞中某点的散射体材料引入点缺陷, 分析其振动能量采集特性, 结果表明单个5 $\times$ 5点缺陷超胞结构共振频带较窄; 为提升俘能效率, 提出两种由3个具有不同缺陷态数量和构型的5 $\times$ 5超元胞结构并联而成的5 $\times$ 15声子晶体板结构, 机电耦合特性分析结果表明: 所提出的局域共振型声子晶体板结构克服了单个点缺陷超胞结构缺陷模过少、共振频带过窄的局限性, 拓宽了俘能器的工作频带, 提高了输出电压; 此外, 引入不同的缺陷态数量和构型, 可以进一步拓宽俘能带宽, 实现更好的俘能效果.      

周期性两相层状带隙材料优化模型

研究并建立了一种在给定频段具有带隙性质的周期性两相层状材料的优化设计模型。首先基于层状材料波传播问题的解析解,得到了波数余弦函数与层状材料微结构参数间的解析表达式。进而分析了波数余弦函数与衰减系数的关系,提出了以波数余弦函数的平方在给定频段的积分为弹性波带隙特性的描述指标,以最大化该指标实现在给定频段使弹性波衰减系数最大化的思想,建立了设计在给定频段具有最优带隙性质的周期性两相层状材料优化提法和求解方法。最后,以几个典型的设计算例为对象,得到了给定微结构尺度约束下在特定频段具有最优带隙性质的材料微结构参数,讨论了材料微结构尺寸对最优材料结构参数的影响,以及最优结构参数对材料带隙性质的鲁棒性,验证了本文优化模型的有效性。     

桁架材料弹性波带隙特性分析

研究了弹性波在周期性桁架材料中的传播特性,并根据桁架材料的周期性特点和杆纵向振动模态,给出了基于单胞的桁架材料弹性波色散(dispersion)方程。分析了1维和2维问题的色散特性,研究了相应的弹性波带隙性质;以CAE分析软件为工具平台对桁架材料的带隙特性进行了数值仿真实验,给出了基于谐响应和特征频率变化特征的仿真实验方法。仿真实验确认了所分析的桁架材料的带隙特性,同时说明所用的仿真实验方法是可行的。     

含有功能梯度材料的一维声子晶体弹性波带隙研究

将功能梯度材料引入声子晶体之中,构成由均匀材料和功能梯度材料交替复合而成的材料常数宏观上呈连续变化的一维声子晶体结构.应用平面波展开法研究了该结构中存在的弹性波带隙特征,并得到前四阶归一化频率带隙结构随材料长度和功能梯度材料指数因子变化的关系图.通过对其带隙结构与不含功能梯度材料的常规声子晶体带隙结构比较可知:功能梯度材料使原有带隙结构发生变化,含有功能梯度材料的声子晶体较常规声子晶体前两阶带隙归一化起始频率升高.这些结果扩宽了功能梯度材料的使用范围,提升了声子晶体工程可靠性,为含有功能梯度材料的声子晶体在工程实际中的应用提供了理论依据和指导.     

Investigation of flexural wave band gaps in a locally resonant metamaterial with plate-like resonators

This paper presents an investigation of flexural wave band gaps in locally resonant metamaterials (LRMs). An LRM is a periodic structure consisting of repeated unit cells containing a local resonator. Due to the local resonance occurring in the unit cell, the LRM induces a band gap (a frequency band in which no waves propagate). Discrete-like or beam-like resonators have generally been used to realise LRMs in previous research. By extending the beam-like resonator configuration, this paper studies LRMs with a plate-like resonator to exploit its advantages with respect to large design freedom. In order to understand flexural wave band gaps in an LRM with plate-like resonators, parametric studies are conducted with the development of a finite element model. Further, the influences of the plate-like resonator design parameters on flexural wave band gaps are investigated. Based on the parametric studies, the rules governing band gap properties are determined. Finally, tailoring flexural wave band gaps by adjusting the parameters is discussed.     

A brief review of metamaterials for opening low-frequency band gaps

Metamaterials are an emerging type of man-made material capable of obtaining some extraordinary properties that cannot be realized by naturally occurring materials. Due to tremendous application foregrounds in wave manipulations, metamaterials have gained more and more attraction. Especially, developing research interest of low-frequency vibration attenuation using metamaterials has emerged in the past decades. To better understand the fundamental principle of opening low-frequency (below 100 Hz) band gaps, a general view on the existing literature related to low-frequency band gaps is presented. In this review, some methods for fulfilling low-frequency band gaps are firstly categorized and detailed, and then several strategies for tuning the low-frequency band gaps are summarized. Finally, the potential applications of this type of metamaterial are briefly listed. This review is expected to provide some inspirations for realizing and tuning the low-frequency band gaps by means of summarizing the related literature.

     

Active elastic metamaterials for subwavelength wave propagation control

Recent research activities in elastic metamaterials demonstrate a significant potential for subwavelength wave propagation control owing to their interior locally resonant mechanism. The growing technological developments in electro/magnetomechanical couplings of smart materials have introduced a controlling degree of freedom for passive elastic metamaterials. Active elastic metamaterials could allow for a fine control of material physical behavior and thereby induce new functional properties that cannot be produced by passive approaches. In this paper, two types of active elastic metamaterials with shunted piezoelectric materials and electrorheological elastomers are proposed.Theoretical analyses and numerical validations of the active elastic metamaterials with detailed microstructures are presented for designing adaptive applications in band gap structures and extraordinary waveguides. The active elastic metamaterial could provide a new design methodology for adaptive wave filters, high signal-to-noise sensors, and structural health monitoring applications.     

压电超构材料及其波动控制研究: 现状与展望

弹性波超构材料是一种人为设计的周期结构材料, 因其独特的力学性能而受到广泛的关注, 在军用和民用领域都展现出重要而独特的应用前景. 根据需求主动或被动地调控弹性波超构材料的力学特性, 能够赋予其更强的适用性能. 其调控的方式多种多样, 其中运用压电材料进行调控是一种方便、速度快、精度高、体积小且价格低的调控方式. 文章中首先简要地介绍弹性波超构材料、可调超构材料、压电材料和几种常用的分流电路的基本特性. 然后依据压电材料在弹性波超构材料中应用形式的不同, 将其分为两大类: 第一类中, 压电材料作为主体结构材料或主体结构的一部分组成材料; 第二类中, 压电材料主要以压电弹簧或压电片的形式贴附于主体结构的表面或内嵌在结构中, 作为激励器或/和传感器. 文章主要介绍两种类型弹性波超构材料的研究内容和发展历史, 涉及带隙调控、波导、负折射、超传输、拓扑态、隐身以及外接分流电路等. 最后总结压电弹性波超构材料研究的不足之处并给出相应的未来研究展望.      

Theoretical investigation of the behavior of an acoustic metamaterial with extreme Young's modulus

A mechanical model with local resonators is proposed as an acoustic metamaterial that exhibits an unusual frequency-dependent effective stiffness. If treated as an equivalent elastic solid, its effective Young's modulus can become unbounded or vanishingly small at two respective frequencies. Moreover, in a certain frequency range, the effective Young's modulus would become negative, resulting in a band gap that coincides with this frequency range. The wave attenuation behavior and mechanism are studied through numerical simulations on the acoustic metamaterial model. The capability of the metamaterial to selectively block or filter unwanted waves is demonstrated by a numerical simulation example.     

Visco-elastic effects on wave dispersion in three-phase acoustic metamaterials

This paper studies the wave attenuation performance of dissipative solid acoustic metamaterials (AMMs) with local resonators possessing subwavelength band gaps. The metamaterial is composed of dense rubber-coated inclusions of a circular shape embedded periodically in a matrix medium. Visco-elastic material losses present in a matrix and/or resonator coating are introduced by either the Kelvin–Voigt or generalized Maxwell models. Numerical solutions are obtained in the frequency domain by means of $\mathbf{k}\left(\omega \right)$-approach combined with the finite element method. Spatially attenuating waves are described by real frequencies ω and complex-valued wave vectors $\mathbf{k}$. Complete 3D band structure diagrams including complex-valued pass bands are evaluated for the undamped linear elastic and several visco-elastic AMM cases. The changes in the band diagrams due to the visco-elasticity are discussed in detail; the comparison between the two visco-elastic models representing artificial (Kelvin–Voigt model) and experimentally characterized (generalized Maxwell model) damping is performed. The interpretation of the results is facilitated by using attenuation and transmission spectra. Two mechanisms of the energy absorption, i.e. due to the resonance of the inclusions and dissipative effects in the materials, are discussed separately.It is found that the visco-elastic damping of the matrix material decreases the attenuation performance of AMMs within band gaps; however, if the matrix material is slightly damped, it can be modeled as linear elastic without the loss of accuracy given the resonator coating is dissipative. This study also demonstrates that visco-elastic losses properly introduced in the resonator coating improve the attenuation bandwidth of AMMs although the attenuation on the resonance peaks is reduced.     

Broadband elastic metamaterial with single negativity by mimicking lattice systems

The narrow bandwidth is a significant limitation of elastic metamaterials for practical engineering applications. In this paper, a broadband elastic metamaterial with single negativity (negative mass density or Young's modulus) is proposed by mimicking lattice systems. It has two stop bands and the bandwidth of the second one is infinite theoretically. The effect of the relevant parameters on band gaps is discussed. A continuum model is proposed and the selection of materials is discussed in detail. It shows that continuum metamaterials can be described accurately by using the lattice model, and the second stopband can be ultra-broad but not infinite. This discrepancy is investigated and a method is provided to calculate the upper limit of the second stopband for a continuum metamaterial. As a verification, the proposed metamaterial is used for wave mitigation over broadband frequency ranges. Moreover, the present method is extended to design 2D anisotropic elastic metamaterials, and a device to control the direction of elastic wave transmission is proposed as an example.