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。     

可重构力学超材料的设计与波动特性研究

力学超材料中的弯曲梁双稳态结构由于其主动调控性强且调控精度高等优点近年来受到广泛关注.文章利用中心受压弯曲梁的不稳定性设计了六角型双稳态结构,首先建立了等效弯曲梁模型,基于梁变形微分方程及能量最低原理探明了结构双稳态特性的产生基理,之后利用有限元数值计算研究了结构几何参数对其整体力学性能的影响,分别得到了具备自恢复及双稳态性能的结构几何参数范围,绘制了几何参数与力学性能之间的相图.同时,可重构结构的可控变形能力有助于调整整体的色散特性,利用数值仿真研究了具备双稳态特性的结构在拉伸和压缩两种构型下的色散关系,对比分析了不同结构几何参数及构型转变对结构产生的带隙位置及范围的影响,之后对由不同构型单胞组成的周期性结构进行了频响分析来验证带隙计算的准确性.通过六角型可重构结构的力学特性、色散特性研究及频响分析表明可以通过结构几何参数的设计实现对结构整体性能的主动调控,为可逆向设计的弹性波超材料结构研究分析提供了一条可靠路径.     

一维声子晶体带隙的非局部辛分析

周期性弹性复合结构(声子晶体)中传播的弹性波存在特殊的色散关系:弹性波只能在某段频率范围内无损耗的传播,该频率范围称为通带.一维声子晶体的色散问题可以看作分层介质中弹性波的传播问题,利用二维弹性理论予以分析.为了研究非局部效应对声子晶体带隙特性的影响,将Eringen的二维非局部弹性理论引入到Hamilton体系下,利用精细积分与扩展的Wittrick Williams算法可获取任意频率范围内的本征解.通过对不同算例的数值计算,分析和对比了非局部理论方法与传统局部理论方法的差别.并进一步指出了该套算法的适用性和优势所在.     

低频弹性波超材料的若干进展

超材料是一类新兴的具有超常物理性质的人造周期/拟周期材料, 能够改变电磁波、声波以及弹性波等在介质中的传播特性. 因在航天、国防以及民用科学等方面的巨大应用潜力, 超材料自被提出后便受到极大的关注并引发研究热潮. 弹性波超材料是超材料的一种, 能够基于弹性波与超材料结构的相互耦合作用实现对弹性波的操控. 带隙是评估弹性波超材料实现弹性波操控的重要工具, 其性质与超材料的材料参数、晶格常数以及局域振子的固有频率相关. 受制于超材料的承载能力、外观尺寸以及局域振子结构等因素, 利用传统超材料开启低频(约100 Hz)弹性波带隙依然存在较大困难. 文章首先简要介绍超材料开启弹性波带隙的基本原理, 然后从低频弹性波超材料基本结构与低频带隙实现方法、低频带隙优化与调控策略、低频带隙潜在应用等三个方面详细总结低频弹性波超材料的研究工作. 其中, 低频带隙超材料的基本结构主要包括布拉格散射型超材料、传统局域共振型超材料以及准零刚度局域共振超材料. 文章通过总结低频弹性波超材料的研究进展, 分析了目前研究中的不足并对未来低频弹性波的研究方向进行了展望.      

二维格栅材料带隙特性分析与设计

周期性材料或结构常表现出阻断特定频段的波传播的特异性质(带隙性质),通过合理设计可以调整带隙的位置和带宽等, 带隙材料在滤波、导波、隔音、隔振等方面有巨大的应用潜力. 据此背景, 研究了材料微结构构型对带隙性质的影响. 分析和比较了三角形、米字形、四边形、六边形、反六边形、Kagome形和钻石形等7种典型拓扑构形格栅材料的带隙性质与弹性波在其中的局部衰减特性, 提出了可表征特定带隙性质的目标函数, 从而对不同构型的材料进行选优; 进一步得到并数值验证了材料微结构中几何参数对带隙性质的影响规律, 为通过改变构型几何参数设计具有特定性质的带隙材料提供参考.      

基于微形态模型的颗粒材料中波的频散现象研究

基于颗粒材料冲击与波动响应特性的调控波传播行为的超材料设计受到广泛关注,设计这类材料需要对颗粒材料的波传播机制及调控机理有深入认识. 波在颗粒材料中传播的频散现象及频率带隙等行为与材料的非均匀性密切相关,通常讨论频散现象是基于弹性理论框架建立微结构连续体或高阶梯度连续体等广义连续体模型来进行. 本研究基于细观力学给出了一个颗粒材料的微形态连续体模型. 在该模型中,考虑了颗粒的平动和转动,且颗粒间的相对运动分解为两部分:即宏观平均运动和细观真实运动. 基于此分解,提出了一个完备的变形模式,得到了对应于不同应变及颗粒间运动的宏细观本构关系. 结合宏观变形能的细观变形能求和表达式,获得了基于细观量表示的宏观本构模量. 应用所建议模型考察了波在弹性颗粒介质的传播行为,给出了不同形式的波的频散曲线,结果显示此模型具有预测频率带隙的能力.      

最优二维固/固声子晶体带隙特性研究

声子晶体是一种具有弹性波带隙特性的周期性复合材料,其带隙特性受单胞拓扑形状的影响。通过拓扑优化技术,能够突破传统设计方法的局限,实现对声子晶体的主动设计。本文基于遗传算法和改进的平面波展开法,通过两阶段的优化过程,得到具有最大相对带隙的二维铜/环氧树脂声子晶体结构,并进一步研究不同带隙最优声子晶体单胞拓扑形状及其带隙特性。结果表明,利用所开发的带隙优化程序,能够得到满足带隙要求的具有全局最优的声子晶体结构;声子晶体最低带隙所对应的单胞是简单晶格结构,其散射体形状简单,而且对应的带隙频率最低,相对带隙最大,对于隔音减振最有实用价值。     

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。     

基于微形态模型的颗粒材料中波的频散现象研究

基于颗粒材料冲击与波动响应特性的调控波传播行为的超材料设计受到广泛关注,设计这类材料需要对颗粒材料的波传播机制及调控机理有深入认识.波在颗粒材料中传播的频散现象及频率带隙等行为与材料的非均匀性密切相关,通常讨论频散现象是基于弹性理论框架建立微结构连续体或高阶梯度连续体等广义连续体模型来进行.本研究基于细观力学给出了一个颗粒材料的微形态连续体模型.在该模型中,考虑了颗粒的平动和转动,且颗粒间的相对运动分解为两部分:即宏观平均运动和细观真实运动.基于此分解,提出了一个完备的变形模式,得到了对应于不同应变及颗粒间运动的宏细观本构关系.结合宏观变形能的细观变形能求和表达式,获得了基于细观量表示的宏观本构模量.应用所建议模型考察了波在弹性颗粒介质的传播行为,给出了不同形式的波的频散曲线,结果显示此模型具有预测频率带隙的能力.     

蜂窝材料的弹性波传播特性

通过研究蜂窝材料的弹性波频散关系,分析了其弹性波传播特性. 采用基于小波理论的分析方法,将材料参数和位移均展开为双正交周期小波基函数的形式,利用Bloch定理将波动方程转化为特征值方程,求解该方程得到3种典型结构------正方、三角与六角排列的铝(Al)和聚丙烯(PP)蜂窝材料的频散关系,并进行了比较分析. 结果显示:结构形式的不同显著地影响其波动特性,而制作材料的不同则没有影响;3种结构形式都不存在完全带隙,但正方和三角形结构在一定的传播方向范围内存在方向带隙,而六角形结构则在任何方向都不存在方向带隙;与正方结构相比,三角结构在相同孔隙率下,在更广的传播方向内和更低的频率下,能产生较宽的方向带隙.      

Extension/Compression-Controlled Complete Band Gaps in 2D Chiral Square-Lattice-Like Structures

Achieving tunable band gaps in a structure by external stimuli is of great importance in acoustic applications. This paper aims to investigate the tunability of band gaps in square-lattice-like elastic periodic structures that are usually not featured with notable band gaps.Endowed with chirality, the periodic structures here are able to undergo imperfection-insensitive large deformation under extension or compression. The influences of geometric parameters on band gaps are discussed via the nonlinear finite element method. It is shown that the band gaps in such structures with curved beams can be very rich and, more importantly, can be efficiently and robustly tuned by applying appropriate mechanical loadings without inducing buckling. As expected, geometry plays a more significant role than material nonlinearity does in the evolution of band gaps. The dynamic tunability of band gaps through mechanical loading is further studied. Results show that closing, opening, and shifting of band gaps can be realized by exerting real-time global extension or compression on the structure. The proposed periodic structure with well-designed chiral symmetry can be useful in the design of particular acoustic devices.     

INFLUENCES OF ANISOTROPY ON BAND GAPS OF 2D PHONONIC CRYSTAL

Band gaps of 2D phononic crystal with orthotropic cylindrical fillers embedded in the isotropic host are studied in this paper. Two kinds of periodic structures, namely, the square lattice and the triangle lattice, are considered. For anisotropic phononic crystal, band gaps not only depend on the periodic lattice but also the angle between the symmetry axis of orthotropic material and that of the periodic structure. Rotating these cylindrical fillers makes the angle changing continuously; as a result, pass bands and forbidden bands of the phononic crystal are changed. The plane wave expansion method is used to reduce the band gap problem to an eigenvalue problem. The numerical example is given for YBCO/Epoxy composites. The location and the width of band gaps are estimated for different rotating angles. The influence of anisotropy on band gaps is discussed based on numerical results.     

Mechanically tunable phononic band gaps in three-dimensional periodic elastomeric structures

Three-dimensional periodic structures have many applications in acoustics and their properties are strongly related to structural details. Here we demonstrate through simulations the ability to tune the phononic band gaps of 3D periodic elastomeric structures using deformation. The elastomeric nature of the material makes the transformation of the band gaps a reversible and repeatable process, providing avenues for the design of tunable 3D phononic crystals such as sonic switches.     

Local resonance phononic band gaps in modified two-dimensional lattice materials

In this paper,modified two-dimensional periodic lattice materials with local resonance phononic bandgaps are designed and investigated.The design concept isto introduce some auxiliary structures into conventional periodic lattice materials.Elastic wave propagation in this kindof modified two-dimensional lattice materials is studied using a combination of Bloch’s theorem with finite elementmethod.The calculated frequency band structures of illustrative modified square lattice materials reveal the existenceof frequency band gaps in the low frequency region due tothe introduction of the auxiliary structures.The mechanismunderlying the occurrence of these frequency band gaps isthoroughly discussed and natural resonances of the auxiliarystructures are validated to be the origin.The effect of geometric parameters of the auxiliary structures on the width ofthe local resonance phononic band gaps is explored.Finally,a conceptual broadband vibration-insulating structure basedon the modified lattice materials is designed and its capability is demonstrated.The present work is anticipated to beuseful in designing structures which can insulate mechanicalvibrations within desired frequency ranges.     

Active control of flexural waves in a phononic crystal beam with staggered periodic properties

The band gaps of a phononic crystal beam with staggered periodic structure are investigated. The periodic system consists of a pure elastic (i.e. PMMA) matrix beam and some piezoelectric (i.e. PZT) patches with coupling between the mechanical–electrical components. The PZT patches connected by negative capacitance circuits are applied to function as the active control system. Based on the condition at the interface between adjacent unit cells, the transfer matrix and localization factor are derived. The influence of the degree of interlacing and negative capacitance circuits are discussed. The numerical results show that another band gap can be generated by the staggered periodic structure of PZT patches. The widths and locations of the band gaps can be changed by the degree of interlacing.     

一维磁电弹准周期结构带隙特性的研究

采用传递矩阵方法,研究了横波(SV波)垂直入射时压电/（弹性/压磁）和（压电/弹性）/压磁两种Fibonacci准周期结构的频带特性,通过计算局部化因子和位移透射系数,数值揭示了此两种Fibonacci准周期结构频带特性的差异以及与相应理想周期结构频带特性的不同,而且表明（压电/弹性）/压磁Fibonacci准周期结构的频带特性与纯弹性材料Fibonacci准周期结构的频带特性是相似的。     

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.     

Size and temperature effects on band gaps in periodic fluid-filled micropipes

A new model is proposed for determining the band gaps of flexural wave propagation in periodic fluid-filled micropipes with circular and square thin-wall cross-sectional shapes, which incorporates temperature, microstructure, and surface energy effects. The band gaps depend on the thin-wall cross-sectional shape, the microstructure and surface elastic material constants, the pipe wall thickness, the unit cell length, the volume fraction, the fluid velocity in the pipe, the temperature change,and the thermal expansion coefficient. A systematic parametric study is conducted to quantitatively illustrate these factors. The numerical results show that the band gap frequencies of the current non-classical model with both circular and square thin-wall cross-sectional shapes are always higher than those of the classical model. In addition,the band gap size and frequency decrease with the increase of the unit cell length according to all the cases. Moreover, the large band gaps can be obtained by tailoring these factors.