一维固液介质准周期结构声子晶体的传输特性

针对一维固液介质的Fibonacci序列准周期声子晶体,利用传输矩阵法研究了弹性纵波在准周期结构中的透射特性。计算结果表明：准周期结构具有比周期结构更宽的禁带,并伴随带边谐振;序列越高,带边谐振越强,并在较低序列的禁带中心出现谐振模;弹性波以0.1rad斜入射时,透射谱向高频方向移动;当固液介质波阻抗接近时,出现等间距的谐振模,同时禁带消失。     

功能梯度压电/压磁双材料的周期界面裂纹问题

研究反平面载荷作用下压电/压磁双材料的周期界面裂纹问题,压电/压磁双材料由有限厚度的功能梯度压电层和功能梯度压磁层粘结而成.为便于分析,假设压电层和压磁层的材料性质沿着裂纹的法线方向呈指数变化,基于分离变量和Hilbert核奇异积分方程方法,获得应力强度因子的数值解.数值算例讨论层厚、周期带长度、梯度参数以及材料参数变动等对应力强度因子的影响.结果发现层厚以及裂纹间距的增大会降低裂纹尖端应力强度因子,梯度参数的改变对应力强度因子也有显著的影响.材料参数变动的讨论发现弹性参数的变动对应力强度因子影响最大,其次为电参数,磁参数的变动对应力强度因子影响最小.     

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.      

横向磁场激励下铁磁梁式板的混沌运动分析

在磁体力分布的磁弹性理论模型和磁场准静态假定模式基础上，对于处在周期时变磁场 中的不可移简支铁磁梁式板非线性磁弹性动力特性进行定性与定量分析．首先利用磁场的摄 动技术和结构变形的模态法，导出了关于模态坐标的非线性动力方程；然后利用Ｍｅｌｎｉｋｏｖ方 法，从理论上给出这一磁弹性动力系统可能出现混沌运动的必要条件及参数范围；最后采用变 步长Ｒｕｎｇｅ－Ｋｕｔｔａ数值积分方法对其磁弹性相互作用的混沌现象进行了定量搜索与模拟，并 利用其轨迹的Ｐｏｉｎｃａｒｅ截面图与Ｌｉａｐｕｎｏｖ指数加以判断．结果表明磁弹性简支梁式板在横 向周期时变磁场中存在混沌吸引子，且在机械阻尼很小时其混沌吸引子表现出稠的特性．     

镜像对称准周期固/液声子晶体的传输特性

以准周期Fibonacci序列为基础,构建了准周期镜像对称结构的一维固液介质声子晶体。利用转移矩阵法,研究了弹性波在所构建的声子晶体中的透射特性。结果表明:弹性波正入射时,转移矩阵与变介质的特性阻抗有关,由于声子晶体结构的局域失谐,在透射谱的中心频率附近对称出现谐振模;对于Q7序列的声子晶体,带隙内谐振模带宽小于10Hz,能实现超窄带声滤波;弹性波斜入射时,带隙向高频区移动;入射角为5°时,谐振模也向高频移动;入射角为10°时,由于谐振的增强,声子晶体结构对频率的选择性提高,使带隙内的谐振模消失。     

附磁压电悬臂梁流致振动俘能特性分析

流致振动蕴含巨大的能量, 本文基于流致振动理论,设计了一种附加磁力激励的压电悬臂梁流致振动俘能器,并通过理论和实验研究其振动俘能特性.该俘能器由压电悬臂梁、圆柱绕流体和磁铁组成;首先基于Euler-Bernoulli梁理论,推导了流致振动附磁压电俘能器的能量函数,利用Hamilton原理建立了流致振动附磁压电俘能器的机电耦合方程;利用数值方法研究详细分析了流速、圆柱绕流体直径和长度、磁间距、磁极和外接电阻等系统参数对压电俘能器振动特性和输出电压的影响.分析结果表明, 该型压电俘能器的振动幅值在低流速条件下产生涡激振动,并产生最大的输出电压;磁力可以降低压电俘能器的共振频率并能够拓宽压电俘能器频带带宽,因此,附磁压电俘能器具有相比没有附磁的压电俘能器更适用于低速层流环境;实验结果与数值结果吻合较好,验证了附磁压电悬臂梁流致振动俘能器的理论分析的正确性.      

附磁压电悬臂梁流致振动俘能特性分析

流致振动蕴含巨大的能量,本文基于流致振动理论,设计了一种附加磁力激励的压电悬臂梁流致振动俘能器,并通过理论和实验研究其振动俘能特性.该俘能器由压电悬臂梁、圆柱绕流体和磁铁组成;首先基于Euler-Bernoulli梁理论,推导了流致振动附磁压电俘能器的能量函数,利用Hamilton原理建立了流致振动附磁压电俘能器的机电耦合方程;利用数值方法研究详细分析了流速、圆柱绕流体直径和长度、磁间距、磁极和外接电阻等系统参数对压电俘能器振动特性和输出电压的影响.分析结果表明,该型压电俘能器的振动幅值在低流速条件下产生涡激振动,并产生最大的输出电压;磁力可以降低压电俘能器的共振频率并能够拓宽压电俘能器频带带宽,因此,附磁压电俘能器具有相比没有附磁的压电俘能器更适用于低速层流环境;实验结果与数值结果吻合较好,验证了附磁压电悬臂梁流致振动俘能器的理论分析的正确性.     

PMN-PT层/弹性基底结构中声表面波特性分析

研究了PMN-PT 压电层/弹性(金刚石) 基底结构中表面波的传播特性,压电层表面是机械自由的,电学边界条件分为电学开路和电学短路,压电层与基底之间采用理想连接. 得到了满足控制方程和边界条件的电弹场以及弹性波在结构中传播时的频散方程,通过数值算例分析了压电材料PMN-PT 的极化方向对弹性波频散曲线和机电耦合系数的影响,以及不同极化方向时弹性位移和电势随结构深度方向的变化,结果可为PMN-PT 压电材料在高频声表面波器件中的应用提供有价值的理论参考.      

反平面剪切状态下压电-压磁夹层结构的圣维南端部效应

本文研究电磁材料层合板圣维南末端效应的衰减特征。考虑压电和压磁构成的三层结构层合板,主要目的是揭示边界条件和材料性能对衰减特性的影响,结果表明,压电压磁性能及边界条件对衰减率有明显影响。     

压电板壳自由振动的三维精确分析

本文简要评述了压电材料板壳结构的研究现状,着重介绍了近年来我们在压电板壳三维分析方面所做的工作：（1）四边简支横观各向同性压电矩形板的状态空间分析方法：（2）横观各向同性压电圆板和环板的状态空间分析方法;（3）横观各向同性压电圆柱壳和球面各向同性压电球壳耦合振动的精确分析。这些工作都直接从压电弹性力学三维基本方程出发,不引进任何变形假设,因此可作为二维简化理论和数值计算方法的校核标准。文末对今后压电材料板壳的研究方向也作了展望。     

ELASTIC WAVE LOCALIZATION IN TWO-DIMENSIONAL PHONONIC CRYSTALS WITH ONE-DIMENSIONAL QUASI-PERIODICITY AND RANDOM DISORDER

The band structures of both in-plane and anti-plane elastic waves propagating in two-dimensional ordered and disordered （in one direction） phononic crystals are studied in this paper. The localization of wave propagation due to random disorder is discussed by introducing the concept of the localization factor that is calculated by the plane-wave-based transfer-matrix method. By treating the quasi-periodicity as the deviation from the periodicity in a special way, two kinds of quasi phononic crystal that has quasi-periodicity （Fibonacci sequence） in one direction and translational symmetry in the other direction are considered and the band structures are characterized by using localization factors. The results show that the localization factor is an effective parameter in characterizing the band gaps of two-dimensional perfect, randomly disordered and quasi-periodic phononic crystals. Band structures of the phononic crystals can be tuned by different random disorder or changing quasi-periodic parameters. The quasi phononic crystals exhibit more band gaps with narrower width than the ordered and randomly disordered systems.     

Band gaps of elastic waves in three-dimensional piezoelectric phononic crystals with initial stress

In this paper, the stop band properties of elastic waves in three-dimensional piezoelectric phononic crystals with initial stress are studied taking the mechanical and electrical coupling into account. The band gap characteristics for three kinds of lattice arrangements (i.e. sc, bcc and fcc) are investigated by the plane wave expansion (PWE) method. Regarding the variables of mechanical and electrical fields as the elements of the generalized state vector, the expression of the generalized eigenvalue equation for three-dimensional piezoelectric periodic structures is derived. Numerical calculations are performed for the PZT-2/polymer and ZnO/polymer phononic crystals. It can be observed from the results that the fcc lattice is more favorable to create the stop band than the sc and bcc lattices for the piezoelectric phononic crystals, which has also been proved for the pure elastic periodic structures. Compared with the PZT-2/polymer systems, the band gap of the sc lattice for the ZnO/polymer structures is narrower. However, the widths of the bcc and fcc lattices for the ZnO/polymer phononic crystals are much larger than those for the PZT-2/polymer structures. The lattice arrangements and the piezoelectricity have remarkable influences on the stop band behaviors.     

Wave band gaps in two-dimensional piezoelectric/piezomagnetic phononic crystals

In this paper, the elastic wave propagation in phononic crystals with piezoelectric and piezomagnetic inclusions is investigated taking the magneto-electro-elastic coupling into account. The electric and magnetic fields are approximated as quasi-static. The band structures of three kinds of piezoelectric/piezomagnetic phononic crystals—CoFe₂O₄/quartz, BaTiO₃/CoFe₂O₄ and BaTiO₃–CoFe₂O₄/polymer periodic composites are calculated using the plane-wave expansion method. The piezoelectric and piezomagnetic effects on the band structures are analyzed. The numerical results show that in CoFe₂O₄/quartz structures, only one narrow band gap exists along the Γ–X direction for the coupling of xy-mode and z-mode for the filling fraction f being 0.4; while in BaTiO₃/CoFe₂O₄ composites, only one narrow band gap exists along the Γ–X direction forxy-mode and no band gap exists for z-mode as the filling friction f is 0.5. Moreover, for the new type of magneto-electro-elastic phononic crystal—BaTiO₃–CoFe₂O₄/polymer periodic composite, the band gap characteristics are more superior in the whole considered frequency regions due to the big contrast of the material properties in the two constituents and the effects of the piezoelectricity and piezomagneticity on the band gap structures are remarkable.     

Folding beam-type piezoelectric phononic crystal with low-frequency and broad band gap

A folding beam-type piezoelectric phononic crystal model is proposed to isolate vibration. Two piezoelectric bimorphs are joined by two masses as a folding structure to comprise each unit cell of the piezoelectric phononic crystal. Each bimorph is connected independently by a resistive-inductive resonant shunting circuit. The folding structure extends the propagation path of elastic waves, while its structure size remains quite small. Propagation of coupled extension-flexural elastic waves is studied by the classical laminated beam theory and transfer matrix method. The theoretical model is further verified with the finite element method(FEM). The effects of geometrical and circuit parameters on the band gaps are analyzed. With only 4 unit cells, the folding beam-type piezoelectric phononic crystal generates two Bragg band gaps of 369 Hz to1 687 Hz and 2 127 Hz to 4 000 Hz. In addition, between these two Bragg band gaps, a locally resonant band gap is induced by resonant shunting circuits. Appropriate circuit parameters are used to join these two Bragg band gaps by the locally resonant band gap.Thus, a low-frequency and broad band gap of 369 Hz to 4 000 Hz is obtained.     

Electro-mechanical coupling wave propagating in a locally resonant piezoelectric/elastic phononic crystal nanobeam with surface effects

The model of a "spring-mass" resonator periodically attached to a piezoelectric/elastic phononic crystal(PC) nanobeam with surface effects is proposed, and the corresponding calculation method of the band structures is formulized and displayed by introducing the Euler beam theory and the surface piezoelectricity theory to the plane wave expansion(PWE) method. In order to reveal the unique wave propagation characteristics of such a model, the band structures of locally resonant(LR) elastic PC Eul...     

Piezoelectric-sensitive mode of lamb wave in one-dimensional piezoelectric phononic crystal plate

We investigate the transmission modes in one-dimensional piezoelectric phononic crystal plate, which is consisted of piezoelectric ceramics placed periodically in epoxy. The influences of piezoelectricity and different electrical boundary conditions on the Lamb waves in the composite plate are studied in detail, and an important elastic wave mode named as piezoelectric-sensitive mode (PSM) is defined. Furthermore, the influences of the piezoelectric constants, the filling fraction and the ratio of thickness to lattice pitch on PSM are given, and the physical mechanism of PSM is also discussed. The numerical results show that PSM has a relatively larger frequency shift and significant change in the displacement distribution when piezoelectricity is considered; the electromechanical coupling coefficient of PSM is much larger than the other modes. It reveals that PSM is an important and useful mode in piezoelectric periodic structures. This investigation is helpful in controlling the band gaps and also gives a potential application in design of sensing system and different piezoelectric devices.     

Shear wave propagation in periodic phononic/photonic piezoelectric medium

Coupled electro-elastic SH waves propagating oblique to the lamination of a one dimensional piezoelectric periodic structure are considered in the framework of the full system of Maxwell’s electrodynamic equations. The dispersion equation has been obtained and numerical analyses carried out for two kinds of composites both consisting of two different piezoelectric materials. The results demonstrate the significant effect of piezoelectricity on the widths of band gaps at acoustic frequencies and confirm that it does not affect the band gaps at optical frequencies.     

WAVE PROPAGATION IN PIEZOELECTRIC/PIEZOMAGNETIC LAYERED PERIODIC COMPOSITES

This paper is concerned with the dynamic behaviors of wave propagation in layered periodic composites consisting of piezoelectric and piezomagnetic phases. The dispersion relations of Lamb waves axe derived. Dispersion curves and displacement fields are calculated with different piezoelectric volume fractions. Numerical results for BaTiO3/CoFe2O4 composites show that the dispersion curves resemble the symmetric Lamb waves in a plate. Exchange between the longitudinal （i.e. thickness） mode and coupled mode takes place at the crossover point between dispersion curves of the first two branches. With the increase of BaTiO3 volume fraction, the crossover point appears at a lower wave number and wave velocity is higher. These findings are useful for magnetoelectric transducer applications.     

Asymptotic Analysis of High-Contrast Phononic Crystals and a Criterion for the Band-Gap Opening

We investigate the band-gap structure of the frequency spectrum for elastic waves in a high-contrast, two-component periodic elastic medium. We consider two-dimensional phononic crystals consisting of a background medium which is perforated by an array of holes periodic along each of the two orthogonal coordinate axes. In this paper we establish a full asymptotic formula for dispersion relations of phononic band structures as the contrast of the shear modulus and that of the density become large. The main ingredients are integral equation formulations of the solutions to the harmonic oscillatory linear elastic equation and several theorems concerning the characteristic values of meromorphic operator-valued functions in the complex plane, such as the generalized Rouché’s theorem. We establish a connection between the band structures and the Dirichlet eigenvalue problem on the elementary hole. We also provide a criterion for exhibiting gaps in the band structure which shows that smaller the density of the matrix is, the wider the band-gap is, provided that the criterion is fulfilled. This phenomenon was reported by Economou and Sigalas (J Acoust Soc Am 95:1734–1740, 1994) who observed that periodic elastic composites whose matrix has lower density and higher shear modulus compared to those of inclusions yield better open gaps. Our analysis in this paper agrees with this experimental finding.     

WAVE LOCALIZATION IN RANDOMLY DISORDERED PERIODIC PIEZOELECTRIC RODS

The wave propagation in periodic and disordered periodic piezoelectric rods is studied in this paper. The transfer matrix between two consecutive unit cells is obtained according to the continuity conditions. The electromechanical coupling of piezoelectric materials is considered. According to the theory of matrix eigenvalues, the frequency bands in periodic structures are studied. Moreover, by introducing disorder in both the dimensionless length and elastic constants of the piezoelectric ceramics, the wave localization in disordered periodic structures is also studied by using the matrix eigenvalue method and Lyapunov exponent method. It is found that tuned periodic structures have the frequency passbands and stopbands and localization phenomenon can occur in mistuned periodic structures. Furthermore, owing to the effect of piezoelectricity, the frequency regions for waves that cannot propagate through the structures are slightly increased with the increase of the piezoelectric constant.