PIEZOELECTRIC METAMATERIALS AND WAVE CONTROL: STATUS QUO AND PROSPECTS
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摘要: 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.Abstract: Elastic wave metamaterial is a kind of artificially designed periodic structure. It has received extensive attention due to its special mechanical properties and has shown valuable and unique application prospects in both military and civilian fields. Actively or passively controlling the characteristics of elastic wave metamaterials according to the needs can endow them with stronger applicability. There are lots of tuning ways, among which using piezoelectric materials is a convenient, fast, high-precision, small-sized and low-cost method. In this article, we first briefly introduced the basic aspects of elastic wave metamaterials, tunable metamaterials, piezoelectric materials and several commonly used shunt circuits. Then, according to the different application forms of piezoelectric materials in elastic wave metamaterials, they are divided into two categories: in the first category, the piezoelectric material constitutes the major structure or acts as a part of the major structure; in the second category, the piezoelectric material is used in the form of a spring or a patch attached to the surface of the major structure or embedded in the structure, acting as an actuator or/and a sensor. We elaborated on the research topics and the development history of the two categories of piezoelectric elastic wave metamaterials, related to band gap regulation, waveguide, negative refraction, super transmission, topological state, cloak as well as shunt circuits. Finally, we summarized the research deficiencies of piezoelectric elastic wave metamaterials and outlined corresponding future research prospects.
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Keywords:
- metamaterial /
- piezoelectric material /
- wave control /
- shunt circuits
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引言
超构材料或超材料(metamaterials)是将精心设计的基本单元通过一定的空间排列来实现普通材料所不具有的奇异或反常性能, 如带隙、波导、负折射、负模量、负密度、超透镜、声学聚焦、声学隐身和拓扑态等[1-2], 已成为一个多学科交叉的前沿研究领域. 过去几十多年来陆续出现的左手材料[3]、光子晶体[4]、声子晶体[5]、时间晶体[6]甚至超表面[7]等都可以归类于超构材料. 超构材料在通信、医学、国防军事、航天航空、遥感等诸多领域都有十分广阔的应用前景. 中国、美国、欧盟、日本和俄罗斯等主要国家和组织都设立了相应的创新研究计划来推动超构材料的基础研究与应用研发[8]: 例如美国F-22战斗机己成功应用具有隐身功能的超构材料天线罩; 欧盟组织了数十位著名学者对超构材料开展联合攻关研究; 日本政府将超构材料技术视作下一代隐形战斗机的核心关键技术, 并拨付巨额资金予以重点研究; 俄罗斯研发了超构材料干扰机天线罩, 并已装备在现代级导弹驱逐舰“激烈号”上. 我国也把发展超构材料研发纳入了国家战略, 如在“十三五”规划纲要中强调要“大力发展超材料等纳米功能材料”. 事实上, 我国于2019年6月4日已正式颁布国家标准《机载超材料天线罩通用规范》(GB/T 37657—2019), 2020年1月1日起正式实施, 这表明超构材料在我国已稳步走向实际应用. 目前超构材料的商业化进程还处于初级阶段, 但据美国n-tech Research (https://www.ntechresearch.com/)发布的报告, 预计在2025年超构材料的市场规模即可达41亿美元, 发展空间很大. 需要强调的是, 常规新材料的研发也是各国重点部署的任务, 只是更着眼于常规性能(如强度、韧性、硬度、力电耦合系数等)的提升.
弹性波超构材料(elastic wave metamaterials), 如声子晶体, 主要调控声波或弹性波在介质中的传播. 弹性波是一种矢量波, 在各向同性波导中, 纵波和横波往往相互作用和纠缠, 使其波动现象远比电磁波和声波复杂, 理论分析较为困难, 因此其研究也更具挑战性[9]. 历史上, 周期结构的研究最早可以追溯到1883年——Floquet研究了波在一维周期结构中的传播问题. Bloch在1928年又将Floquet的结论推广到三维结构中, 得到了著名的Bloch定理. 1946年, Brillouin在其著作《Wave Propagation in Periodic Structures》中详细地研究了周期弹簧−质量系统的振动特性[10]. 直到1993年, Kushwaha等[5]研究二维复合材料时, 根据这类周期结构的声学与振动特征, 首先提出了声子晶体的概念. 早期研究的声子晶体所形成的禁带大多是由Bragg散射机制引起的. Liu等[11]在2000年研究橡胶、铅和环氧树脂构成的三维晶体, 揭示了新的禁带产生机理, 即局域共振机理. 该机理允许“小尺寸控制大波长”, 更满足实际应用需求, 为超构材料的研究打开了新的疆域. 值得指出的是, 基于局域共振机理的超构材料对微结构周期性的要求并不严格, 但本文聚焦于具有周期性的弹性波超构材料.
超构材料一般是选择已有材料, 通过设计新的微结构来实现优越而奇异的性能, 在材料选择时有一定的规律可以遵循: 高/低模量一般对应高/低工作频率; 不同组分相之间阻抗差异大一般对应更宽带隙; 为了进行主动调控, 一般会选择压电材料、形状记忆合金、磁流变液等智能材料, 等等.
总之, 超构材料利用人工结构的精心构筑实现超常性能, 为高性能功能材料的研发确立了崭新模式, 为超常规器件的研制提供了理论指导, 既有重要的科学价值, 也有巨大的应用前景. 虽然从左手材料的概念提出至今, 超构材料的研究历史已将近一甲子, 但事实上只在最近20年左右其研究才真正得到了蓬勃发展, 被评为21世纪前10年10项重大突破之一[12]. 特别是最近十余年来, 随着“拓扑”概念与超构材料的深入结合, 由量子力学所预测的独特现象在宏观材料体系上得到证实, 进一步增强了人们对超构材料的研究热情[13].
1. 可调弹性波超构材料
1.1 弹性波超构材料的可调性
弹性波超构材料的可调性能使其更好地适应环境变化, 拓宽工作频率范围, 克服被动式超构材料单频或窄频工作的严重缺点[14]. 可调超构材料的研究始于Goffaux和Vigneron[15]的研究, 他们于2001年针对流固系声子晶体提出将非轴对称的固体散射体转动一定的角度以改变禁带宽度. 除了通过旋转散射体调控超构材料力学特性外[16-18], 施加外界载荷改变结构的刚度或形状也是一种有效方法[19-23], 如Bertoldi等[24-25]通过压缩具有负泊松比的多孔软材料结构以达到拓宽禁带的目的.
目前可调超构材料的一个研究方向是利用智能材料(多场耦合材料)设计主动式或者智能超构材料, 赋予超构材料智能化的同时, 也将扩大其功能范围, 使相关器件同时具备多种优越性能, 有效地推动器件的集成化、小型化和多功能化. 通过独特的设计, 常见的智能材料几乎都可以用于智能超构材料, 如形状记忆合金[26-27]、介电高弹体[28-29]、磁致伸缩材料[30-32]、电流变液[33-35]、磁流变液[33, 36-37]、光敏材料[38-39]和压电材料等.
1.2 压电材料在可调弹性波超构材料中的应用
在众多智能材料中, 压电材料毫无疑问是研究最充分、技术最成熟、应用最广泛的智能材料. 无论是厚重坚硬的压电陶瓷或合金、还是轻质柔软的聚合物, 无论是导体还是半导体, 无论体积大小, 无论低频还是高频, 都能找到压电材料的踪影或应用. 常见的压电材料可分为压电晶体(如石英晶体)、压电陶瓷(如锆钛酸铅PZT)以及压电聚合物(如聚偏氟乙烯PVDF)三大类, 三类压电材料各有优缺点, 在不同领域都有独特的应用价值. 压电材料最显著的特点是存在力电耦合效应[40]: 在机械荷载的作用下会出现表面电荷并在体内形成电场(正压电效应), 也可以在电场作用下产生变形(逆压电效应). 这一力电耦合特性赋予了压电材料在电能和机械能之间进行转换的能力, 从而在换能器、传感器和激励器等应用中大显身手. 与其他智能材料相比, 压电材料具有响应速度快、控制精度高、体积小、市场大、价格便宜等突出优点.
图1展示的是压电声子晶体和压电超材料的研究文献数量随年份变化趋势以及学科分布情况(数据来源于2021年05月的Scopus数据库, 检索方式为: 标题、摘要和关键词中检索“piezoelectric”, 且全文检索“phononic”或“metamaterial”或“phononic和metamaterial”).
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图 1 压电声子晶体和压电超材料(a)研究文献数量趋势及(b)学科分布情况Figure 1. (a) Trends in the number of research documents and (b) discipline distribution on piezoelectric phononic crystals and piezoelectric metamaterials2. 压电分流电路
压电材料优异的力电耦合效应使得利用不同的外接电路改变压电材料力学性能进而调控超构材料各方面特性成为可能. 设计电路最关键的问题在于寻找简单且有效的方式来控制结构的振动, 而理想的控制电路具有稳定性、低能耗以及针对系统参数变化的鲁棒性.
已有不少文章详细地分析对比了常见的几种压电分流电路[41-42], 其电路图以及特点分别汇总于图2和表1. 当外接电路中仅有电阻元器件时, 称为电阻分流电路[43-44], 压电材料的机械振动转化为电路中的电能, 部分能量以热能的形式耗散. 若同时串联或并联地接入电阻和电感, 则形成谐振单模分流电路[44-47], 如果电路的谐振与机械系统的谐振相等, 则电路将处于谐振状态, 并且将产生相当大的控制力来抵抗机械系统的振动; 对应地, 谐振多模分流电路[48-50]则可以调控更多频段的机械振动.
表 1 常见压电分流电路总结Table 1. Summary of common piezoelectric shunt circuitsCircuit Characteristics resistive shunts (R) passive (or autonomous), simple structure, low cost, but low damping effectiveness resonant single-mode shunts (RL) passive, simple structure, in-series or in-parallel, resonant shunts, effective vibration attenuation but only one narrow range, require large inductance in low frequency resonant multi-mode shunt circuits passive, effective in multiple frequency bands compared to single-mode, but much more complicated and expensive as the mode increases negative capacitance shunts (NC) semi-active, continuously adjust large frequency bands, both high frequency and low frequency, various application forms, but more complicated and unstable adaptive shunt circuits perform online adaption of their impedance, always combine with other shunt circuit, as adaptive RL-shunt、adaptive RLCN-shunt circuit et al. synchronized switch damping
shunt circuits (SSD)semi-passive, nonlinear, turned on and off synchronously with the structure vibration period, adapt to different excitation frequencies、such as SSDS\SSDI\SSDNC\SSDV\SSDCI, but arising the higher order harmonics 通过图2(d)左图中的电路能够实现负电容(negative capacitance, NC)[51]. 负电容能够抵消压电换能器中固有的电容, 从而使得在电阻中的能量耗散最大化. 利用负电容分流电路[52-58]调控是最近得到特别关注的一个研究热点. 通过与压电片的连接, 负电容分流电路一方面可以有效改变压电材料的等效刚度[59-60], 另一方面可以在很大范围内连续改变系统的阻尼, 产生很好的阻尼效应[61-63], 从而使其在结构振动控制中突显出一定的优越性. 需要注意的是, 环境以及需求的变化可能会导致结构共振频率发生巨大改变, 同时温度也会引起控制电路中电容发生改变, 影响分流电路的调节性能, 而自适应分流电路[64-65]能够克服该困难. 同步开关阻尼分流电路[66-71]是一种半主动控制方法, 根据结构振动频率周期性地打开或关闭开关, 等效于提供一个非线性的冲击载荷, 这种分流电路不需要对被控结构进行精确的系统辨识, 振动控制效果较好并且稳定性高, 外界环境的改变对控制系统影响较低, 最主要的是控制系统简单, 仅需要较少的电子元器件即可实现[72].
3. 压电弹性波超构材料研究进展
到目前为止, 压电超构材料可按压电材料的使用方式分成两种不同的类型(如图3所示, 其中橙色为压电材料, 蓝色为其他材料, 黑色代表质量块): 第一类是将压电材料作为超构材料的主体材料(包含作为多组元声子晶体中的一种材料相); 第二类是制成压电弹簧或以压电片的形式粘贴在弹性主体结构的表面或内嵌在主体结构中作为传感器或/和激励器. 接下来将介绍两类压电超构材料的研究内容与研究进展.
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图 3 两类压电超构材料示意图Figure 3. Schematic diagrams of two categories of piezoelectric metamaterials3.1 第一类压电超构材料研究进展
Wilm等[73]于2002年首先考察了压电复合材料声子晶体中波的传播, 但他们将侧重点放在了平面波展开法的应用和推广上, 并未探讨压电材料对力学特性的调控作用. 次年, 他们又研究了嵌入石英棒的环氧树脂结构[74], 给出了面外波的能带结构, 并指出使用该复合材料作弹性波导的建议. Hou等[75]研究了由压电陶瓷和聚合物组成的弹性复合材料, 通过比较具有和不具有压电效应的弹性带结构, 发现当压电材料填充比例较小或仅考虑低频区域时, 压电效应可以忽略; 压电相填充率(或体分比)较大时, 压电效应可增大全带隙宽度. Laude等[76]和Wu等[77]分别考察了不同构型的压电声子晶体半空间, 讨论了表面波模态的存在条件和力电耦合的影响. Hsu和Wu[78]则分析了Bleustein−Gulyaev−Shimizu表面波的传播特性. 此后, 压电声子晶体的研究得到了更多的研究者的关注, 研究兴趣稳步上升.
早期大多数的研究都是将力电耦合效应纳入到分析模型中, 考察其对不同结构的压电声子晶体中不同模态波(体波、表面波、板波等)传播的影响, 并以此为据设计可调弹性波器件. 有学者在该领域中作了大量工作, 比如受预应力的周期压电杆结构[79]、二维周期分层压电复合结构[80-81]失谐时面内波(或瑞利波[82])的传播和局域化行为; 压电材料对二维[83-84]、三维[85]超构材料以及不同形状的夹杂[86]对声子晶体带隙的调节作用(如图4所示). Zou等[87]发现二维压电声子晶体的第一阶带隙与填充率和极化方向等因素有关; 此外, 通过不同的外接电路可以主动控制压电超构材料的带隙特征[88], 如Wang等[89]通过LC外接电路精确且面向目标地控制低频Lamb波的带隙. Ponge等[90]用压电声子晶体设计了可调的Fabry−Perot谐振器. Hou与Assouar[91]则设计了具有负弹性模量的压电超构材料来调节带隙. Lian等[92]提出了一种改进的平面波展开法, 用于计算外接分流电路的压电声子晶体的带隙特征. 在具有力电耦合效应的压电超构材料中, 还可以进一步引入压磁材料, 实现电能、机械能、磁能的相互转换, 通过力−电−磁多场耦合效应优化超构材料的带隙[83,93-94]或隐身[95]等特性.
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运用压电材料除了能设计带隙可调的智能超构材料, 还能探究波的局域化[96]、单向传输[97-98]和波导[99]等特性. 如Lan和Wei[96]分析了压电效应和弱界面对层状压电声子晶体带隙的影响规律, 发现弱界面会降低带隙频率, 并产生波的局域化行为. Zheng等[97]则介绍了一种使用非线性压电元结构操纵单向弹性波传输的新颖方法, 并从实验上研究了超传输现象, 如图5所示. Oh等[99]设计的一个由PZT-5A压电杆周期排布在硅胶基体中形成的压电声子晶体波导, 通过在压电杆上施加不同的电学条件, 即可形成所需要的弹性波传播路径.
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当前第一类压电超构材料研究有若干方向值得关注. 第一, 将共振单元等一些特殊的微结构或相关的概念(包括拓扑声学)引进来, 推动了压电超构材料微结构−波动性能−声学器件的一体化设计与多功能化实现[100-105]. 如Zhou等[105]提出了一种在A-B-A串联结构的压电杆系统中生成主动可调拓扑保护界面态的创新方法(如图6所示), 发现改变某一路径上的电容会导致拓扑相变, 同时电容器的不同变化路径会导致拓扑相变点的位置不同. 第二, 将拓扑优化的方法引入到压电超构材料的设计中来[106], 有望进一步拓展压电超构材料的设计版图与功能版图. 第三, 与压电材料类似, 软介电材料在预变形后也具有表象的力电耦合性能, 使之在满足现代器件柔顺化要求之上, 也具备了主动适应环境的能力, 软介电超构材料及其波动控制的研究也因此而成为一个值得探索的新方向[107-110]. 如Wu等[111]设计了一种由介电弹性体制成的软圆柱声子晶体, 发现电压和预拉伸可以分别改变带隙的宽度和位置.
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3.2 第二类压电超构材料研究进展
第二类的压电超构材料研究也非常丰富, 其早期的脉络显然出自结构控制这一领域[112-113]. 通常粘贴于主体结构之上的压电片会与电路相连接, 不同的电路设计将导致不同的控制效果, 从而带来了极大的灵活性. Thorp等[114]首先提出利用压电分流阻尼(piezoelectric shunt damping)来强化波的衰减特征, 其要点是利用分流电路形成局域共振型带隙. 此后, 很多学者将不同的线性或非线性压电分流电路应用于不同的超构材料, 取得了很多理论进展, 也有一部分成果得到了实验的验证, 显示出该方法的简便性和有效性[115-123]. Casadei等[124]首次提出用压电片来实现波导的新颖方法. 出于相同的目的, Celli和Gonella[125]在二维蜂窝状结构中粘贴压电片来控制弹性波朝不同的方向传播. Cardella等[126]通过在梁上布置压电片的方式实现可调的“彩虹陷阱”[127]. 在此工作基础上, Celli等[128]通过在二维网状结构上布置压电片来控制不同方向和频率的弹性波, 以实现传播路径的控制. Maurini等[129]研究了由分布式压电装置制成的用于控制梁振动的电子减振器. Baz等[130-137]用压电薄片周期性地隔开流体腔的方式, 在主动控制等效密度和刚度的一维声学超结构方面做了大量系统性工作. 利用压电超构材料在实现可主动控制的负折射成像[138]、自适应GRIN (gradient index)透镜[139]以及声学隐身斗篷[140-142]等方面也取得了诸多进展. 如Ning等[143-144]通过在超构材料板上粘贴外接负电容电路的压电片(如图7), 可有效提升弹性波隐身及黑洞行为、明显扩大隐身及黑洞特性的频率区间, 使得此类结构呈现灵活的主动控制能力.
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利用负电容分流电路是最近得到特别关注的一个研究热点, 通过负电容分流电路可以控制梁[145]、板[146]或层状声子晶体[147-148]等结构中纵波或弯曲波传播, 并主动地调控其带隙特征. Chen等[149-150]首次采用负电容分流电路来调控如图8所示的内嵌质量晶格(mass-in-mass lattice)声子晶体, 不仅可以获得负的等效模量, 而且可以有效扩大带隙范围. Lee和Balint[151]将负电容分流电路与简单的电阻−电感电路进行了比较, 发现前者在产生宽带隙方面优势明显. Zhou等[152]利用负电容分流电路, 结合局域共振单元概念, 设计了一种特殊的梁结构, 使负电容具有增强共振分流效应(NCER), 产生增强超阻尼现象[153], 从而获得极宽的低频带隙, 如图9所示. Li等[154]针对3D打印的超材料, 采用负电容分流电路控制波的传播路径, 模拟和实验都验证了其良好的效果. Trainiti等[155]利用负电容电路时间周期性调控压电片刚度, 从理论和实验上实现弹性波单向滤波效果. 类似的研究还可见于Marconi等[156]的工作. Li等[157]在由六边形晶格构成的压电超材料板上引入负电容电路, 通过主动控制产生了原本不具备的拓扑特性, 且呈现了良好的弹性波拓扑免疫性能. 最近, Hu等[158]从理论上揭示了负电容分流电路在导致多带隙这一点上等价于一个耦合弹簧的作用.
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以上工作的重点可分为两大部分: 一部分是设计新颖的结构实现特殊功能器件; 另一部分是利用不同的电路达到不同的控制效果. 但压电材料的正/逆压电效应没有得到充分的运用: 即压电片同时作为激励器和传感器, 通过采集传感器的信号, 反馈给激励器, 形成闭合回路, 实现更智能的控制效果. 这类研究其实已有长期的理论与实践基础[159-166], 主要集中在工程应用、材料科学和机器人等领域, 但在压电超构材料中的研究尚且不多. 在这方面取得较好进展的是与超表面有关的研究. 例如, Chen等[167]利用压电片的传感与激励功能设计了前馈控制回路, 以精确控制散射波/透射波的相位、波幅等重要参量, 实现了多种声学功能(如波导、聚焦和隐身). Popa等[168]基于同样的原理实现可调的弹性波透镜. 最近, Ren等[169]提出了一种新颖的主动弹性超构材料板, 通过沿板的一个方向上周期性布置的压电激励器和传感器实现可调节的带隙特性.
如上所述, 由于外接电路的多样性和基于常规弹性材料的主体结构制作的简便性, 第二类压电超构材料的研究最近得到了较多的关注. 有时, 两类超构材料的边界也不是如此清晰. 例如, Degraeve等[170]考察了由同一均匀压电材料短柱组成的一维声子晶体杆结构, 在短柱和短柱之间镶嵌力学上可忽略的电极(即不计其刚度效应和质量效应), 从而可以在短柱两端施加不同的电学条件或外接不同的电路. Hu等[171]在压电矩形柱的一对表面涂覆电极并外接电路, 同样可以达到有效控制波传播路径的目的.
4. 不足与展望
从上述回顾可以看出, 压电超构材料因其力电耦合特性和多样化的外接电路控制方式而在弹性波控制方面具有突出的优势. 事实上, 传统的弹性波激发、接收及控制多依赖于压电声波器件[172]. 因此, 基于压电材料研发具有优越性能的超构材料并进而应用于弹性波的控制是非常自然的选择, 将为实验验证和原型器件的研发带来极大的方便. 从研究现状来看, 目前该方向至少存在以下四点不足之处:
(1)具有微结构的非均匀材料的动态均匀化理论一直未有很好的突破, 从而使现有的压电超构材料性能的研究大多数只能依赖于数值模拟手段[173].
(2) 3D打印技术为个性化、精细化的微结构制备提供了重要手段[174], 但目前结合压电超构材料的研究尚不多见.
(3)已有压电材料本身性能还存在不足, 有可能成为压电超构材料进一步推广应用的障碍. 压电超构材料中常用的压电材料如锆钛酸铅(PZT)压电性强、介电常数高、灵敏度高, 但硬而脆, 容易断裂且有毒性; 压电聚合物(如聚偏二氟乙烯PVDF)虽压电性好、密度低、杨氏模量低, 在柔软器件上能发挥作用, 但其难以极化和机电耦合系数低的缺点也限制了应用范围, 等等.
(4)外接电路的灵活性和多样化使得压电超构材料性能的调控方式极为方便和丰富, 调控效果也十分突出. 从现有的研究来看, 一方面受制于现有的外接控制电路的缺陷, 以及缺少对力学信号高效采集、处理和反馈的手段, 另一方面压电材料作为传感(正压电效应)和激励(逆压电效应)的双重特性并没有被完全利用起来, 因此高效控制的潜力还没有得到充分挖掘.
针对以上四点不足, 相应的展望如下:
(1)随着微结构形式的逐步拓展(如将机构引入到微结构中; 在某种意义上看, 不同的外接电路也可以看成是微结构的一种), 各种新型超构材料不断出现, 在时空两个维度都可以实现复杂的性能变化, 从而使相应的波动现象越来越丰富多彩, 其调控的可能性和需求也随之增强. 这种情况下尤其需要建立动态均匀化方法[175], 将复合材料的微观结构与其频率相关的动态有效特性联系起来, 以快速指导压电超构材料的设计并推动实际应用. 简言之, 均匀化理论将非均匀的复合材料等价为一个均匀介质, 二者在合适的平均意义下具有相同的性能. 其中Willis等效介质理论[176-177]是一个可行的方向, 该理论是在对随机介质进行等效分析的基础上发展的, 且表明物质点的有效响应在空间和时间中是非局部的, 它预测了弹性超构材料的有效速度可以引起有效应力, 而有效应变可以引起有效动量. Willis等效介质理论还在不断完善中[178-180]. 对于压电超构材料, 需额外考虑压电超构材料所特有的力电耦合效应及更复杂的波与微结构相互作用. 另外, 由于在压电超构材料设计方面尚缺少体系简单且适用性广的连续介质力学理论, 因此在实验表征方面也存在着根本性的理论缺陷, 亟需弥补.
(2)采用基于弹性材料的3D打印获得特定的微结构, 再粘贴压电片进行波动控制的方式为压电超构材料和智能波动器件的制作提供了一条重要途径[154]. 但是, 压电片的粘结与外接电路的连接等尚需手工完成, 而且仅限于外表面粘贴, 这极大地限制了压电超构材料性能控制与优化范围. 另外, 第一类压电超构材料的3D打印研制也只有个别报道(见文献[174], 其打印精度在百微米量级), 而直接利用压电材料构筑超构材料主体结构, 有可能带来更多优异/奇异的物理力学性能[174, 181-183]. 另外, 4D打印[184]技术的可喜进展[185]也给高性能压电超构材料研发版图的扩展带来了新的方向.
(3)开发性能更优的压电材料, 为压电超构材料的构筑提供更多元的选择. 如压电陶瓷和聚合物等两相或多相材料构成的压电复合材料(如PVDF-PZT复合材料[186])同时具备压电陶瓷与压电聚合物的优点: 与传统的压电陶瓷或压电单晶相比, 它具有更好的柔顺性和机械加工性能, 且密度更小、韧性更好; 与压电聚合物相比, 其压电常数和机电耦合系数较高, 因此灵敏度较高. 通过改变不同材料相的占比, 还可以在一定程度上调节压电复合材料的宏观材料参数. 此外, 压电材料与磁致伸缩材料组成的复合材料还具有磁电效应, 从而可以利用磁场进行非接触式控制.
(4)为了充分利用压电材料的性能, 还需要开发对力学信号快速且精确处理的设备; 设计更优异的外接控制电路(稳定性好, 调节精确且范围大, 体积小, 能耗低等); 在更一般形式的压电超构材料中充分利用压电材料所固有的正/逆压电效应, 实现反馈控制. 将为高性能智能超构材料及可调声波器件的研制提供更经济、更优化、更多样、更主动的方案选择. 需要指出的是, 在压电超构材料中可能存在各种各样的材料界面[187], 可能会导致常规数值方法的失效[188], 因此在压电超构材料的设计中也要重视高效、稳定和精确的数值计算方法的研究.
5. 结语
超构材料独特的力学性能引起了人们的广泛关注, 而可调超构材料能够根据环境和需求的变化改变自身特性, 从而极大地提升相应器件的适用性. 采用拥有多场耦合特性的智能超构材料能够拓展可调结构的设计空间, 并丰富调控手段.
压电材料具有优异的力电耦合效应, 而外接分流电路调节方便且设计方式多样, 两者结合可使相应的压电超构材料具有丰富可控的波动特性, 从而满足不同的声波器件功能设计与应用需求. 本文在简要介绍压电超构材料及常见控制电路的特点后, 根据压电材料应用形式的不同, 将压电超构材料分为两大类, 并分别介绍了两类压电材料的研究内容及特点. 最后从理论、制备、新型压电材料开发和高效控制四个方面分析了压电超构材料现有研究的不足之处并给出了相应的展望. 随着现代科技的发展, 压电超构材料的研究将逐步发展完善, 并最终将在军用和民用的各个领域得到普遍的应用.
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图 1 压电声子晶体和压电超材料(a)研究文献数量趋势及(b)学科分布情况
Figure 1. (a) Trends in the number of research documents and (b) discipline distribution on piezoelectric phononic crystals and piezoelectric metamaterials
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图 3 两类压电超构材料示意图
Figure 3. Schematic diagrams of two categories of piezoelectric metamaterials
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表 1 常见压电分流电路总结
Table 1 Summary of common piezoelectric shunt circuits
Circuit Characteristics resistive shunts (R) passive (or autonomous), simple structure, low cost, but low damping effectiveness resonant single-mode shunts (RL) passive, simple structure, in-series or in-parallel, resonant shunts, effective vibration attenuation but only one narrow range, require large inductance in low frequency resonant multi-mode shunt circuits passive, effective in multiple frequency bands compared to single-mode, but much more complicated and expensive as the mode increases negative capacitance shunts (NC) semi-active, continuously adjust large frequency bands, both high frequency and low frequency, various application forms, but more complicated and unstable adaptive shunt circuits perform online adaption of their impedance, always combine with other shunt circuit, as adaptive RL-shunt、adaptive RLCN-shunt circuit et al. synchronized switch damping
shunt circuits (SSD)semi-passive, nonlinear, turned on and off synchronously with the structure vibration period, adapt to different excitation frequencies、such as SSDS\SSDI\SSDNC\SSDV\SSDCI, but arising the higher order harmonics 
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