不均匀磁电弹板中的厚度扭曲波的传播

压电-压磁复合材料或结构的许多应用是与弹性波的传播密切相关的,这要求人们首先从理论的角度弄清楚弹性波的传播规律。本文研究由多个不均匀磁电弹介质组成的薄板厚度扭曲波的传播性质,从磁电弹全耦合场三维方程出发得到了其精确解,根据所得到的解分析了波的传播特征,这些结果对于理解和设计谐振器、滤波器以及声波元件提供了有价值的理论基础。     

偏压电场作用下磁电弹板中Lamb波传播研究

基于磁电弹性材料的本构关系和运动微分方程,研究了磁电弹板中Lamb波的传播特性.在电磁开路和短路两种边界条件下,导出了偏压电场作用下磁电弹板中Lamb波的对称模态和反对称模态的相速度方程,求解了相应的应力场.通过数值算例分析了偏压电场对相速度和应力场的影响.结果表明,偏压电场对相速度有较大影响,对应力场几乎没有影响.研究成果可为设计磁电换能器提供一定的理论参考.     

功能梯度磁电弹耦合结构中的间隙波

研究了由均匀磁电弹半空间和功能梯度磁电弹层组成的耦合结构中间隙波的传播特性.假定功能梯度层的材料性能沿厚度方向呈指数变化,且其表面机械自由,但承受两种电磁边界条件.首先推导了频散方程,然后结合数值算例分析了功能梯度层材料性能的梯度变化、厚度及电磁边界条件对相速度的影响,结果对功能梯度磁电弹材料在声波器件中的应用具有参考价值.      

GAS WAVE IN FUNCTIONALLY GRADED MAGNETO-ELECTRO-ELASTIC COUPLED STRUCTURE

研究了由均匀磁电弹半空间和功能梯度磁电弹层组成的耦合结构中间隙波的传播特性.假定功能梯度层的材料性能沿厚度方向呈指数变化,且其表面机械自由,但承受两种电磁边界条件.首先推导了频散方程,然后结合数值算例分析了功能梯度层材料性能的梯度变化、厚度及电磁边界条件对相速度的影响,结果对功能梯度磁电弹材料在声波器件中的应用具有参考价值.     

功能梯度材料板中Lamb波传播特性研究

对材料性能参数沿厚度连续变化的横观各向同性热应力缓和型功能梯度材料板中Lamb波的传播问题,采用幂级数法,求得其相速度方程.借助数值算例,分析了参数梯度变化对Lamb波频散曲线的影响,并与相应陶瓷板和金属板中的频散曲线进行了对比.进一步研究了参数梯度变化对波结构的影响,揭示了Lamb波在这种非均质板中的传播行为,所得结果可以为功能梯度材料及结构的超声表征与检测提供理论依据.     

磁场对电磁弹性板中Lamb波频散特性的影响

研究了静态磁场下电磁弹性结构中Lamb波的传播行为.在确定静态磁场下电磁弹性板中耦合初始广义应力(弹性应力、电位移和磁感应强度的基础上,推导了含初始广义应力时板中Lamb波传播的运动方程,并由此获得了对称模态和反对称模态时的频散方程.以由BaTiO3-CoFe2O4材料构成的电磁弹性板模型作为数值算例,绘制了Lamb波传播的对称模态和反对称模态频散曲线.计算结果表明磁场对Lamb波的频散特性有一定的影响.     

含孔软铁磁材料Mindlin板中弹性波散射问题

基于考虑磁弹相互作用的Mindlin板弯曲波动方程，采用波函数展开法，分析研究 了含孔软铁磁材料Mindlin板中弹性波散射与动应力集中问题，给出了问题的分析 解和数值算例. 通过分析发现：磁感应强度对动弯矩集中系数和动剪力集中系数有 增加的作用，特别是在低频的情况下.     

双材料界面裂纹复应力强度因子的正则化边界元法

双材料界面裂纹渐近位移和应力场表现出剧烈的振荡特性, 许多用于表征经典平方根($r^{1/2})$和负平方根($r^{-1/2})$渐近物理场的传统数值方法失效, 给界面裂纹复应力强度因子($K_{1} +{i}K_{2} )$的精确求解增加了难度. 引入一种含有复振荡因子的新型"特殊裂尖单元", 可精确表征裂纹尖端渐近位移和应力场的振荡特性, 在避免裂尖区域高密度网格剖分的情况下, 可实现双材料界面裂纹复应力强度因子的精确求解. 此外, 结合边界元法中计算近奇异积分的正则化算法, 成功求解了大尺寸比(超薄)双材料界面裂纹的断裂力学参数. 数值算例表明, 所提算法稳定, 效率高, 在不增加计算量的前提下, 显著提高了裂尖近场力学参量和断裂力学参数的求解精度和数值稳定性.      

梯度波阻板的地基振动控制研究

波阻板(wave impeding block,WIB)隔振体系是一种有效的振动污染治理措施,虽逐渐被应用在工程实际中,但以往的研究多集中于单相固体均质材料的情形,而对材料特性沿空间连续变化的非均匀固体材料的波阻板隔振性能的研究相对较少.基于功能梯度材料(functionally graded material,FGM)特点,本文提出了以功能梯度波阻板作为隔振屏障的一类新型的地基振动控制体系.考虑在弹性地基内部设置梯度波阻板,基于线弹性理论,利用傅里叶积分变换,根据Helmholtz矢量分解原理,建立了弹性地基在动载荷作用下的回传射线矩阵法(reverberation ray matrix method,RRMM)计算列式.假设梯度波阻板的物理力学性质沿深度方向按幂函数连续变化,采用数值傅里叶逆变换获得了弹性地基的位移和应力等物理量的数值解.通过数值算例,与单相固体均质波阻板进行了对比,并分析讨论了梯度波阻板的材料梯度因子、埋深以及梯度波阻板厚度等物理力学参数对地基隔振性能的影响规律.结果表明,梯度波阻板能有效降低振动的振幅,与单相固体均质波阻板相比,梯度波阻板具有更好的减振隔振效果.地基的位移幅值和应力幅值随着梯度因子的增大而减小.梯度波阻板的隔振效果随着波阻板厚度的增大而提高,而随着梯度波阻板埋深的增大而降低.     

功能梯度材料明德林矩形微板的热弹性阻尼

功能梯度材料微板谐振器热弹性阻尼的建模和预测是此类新型谐振器热?弹耦合振动响应的新课题. 本文采用数学分析方法研究了四边简支功能梯度材料中厚度矩形微板的热弹性阻尼. 基于明德林中厚板理论和单向耦合热传导理论建立了材料性质沿着厚度连续变化的功能梯度微板热弹性自由振动控制微分方程. 在上下表面绝热边界条件下采用分层均匀化方法求解变系数热传导方程, 获得了用变形几何量表示的变温场的解析解. 从而将包含热弯曲内力的结构振动方程转化为只包含挠度振幅的偏微分方程. 然后,利用特征值问题在数学上的相似性,求得了四边简支条件下功能梯度材料明德林矩形微板的复频率解析解, 进而利用复频率法获得了反映谐振器热弹性阻尼水平的逆品质因子. 最后, 给出了材料性质沿板厚按幂函数变化的陶瓷?金属组分功能梯度矩形微板的热弹性阻尼数值结果. 定量地分析了横向剪切变形、材料梯度变化以及几何参数对热弹性阻尼的影响规律. 结果表明, 采用明德林板理论预测的热弹性阻尼值小于基尔霍夫板理论的预测结果, 而且两者的差别随着相对厚度的增大而变得显著.      

Propagation of thickness-twist waves in a multi-sectioned piezoelectric plate of 6 mm crystals

We study thickness-twist vibrations and waves in an unbounded, multi-sectioned piezoelectric plate of crystals with 6 mm symmetry or polarized ceramics. An exact solution from the three-dimensional equations of piezoelectricity is obtained. Basic vibration and wave propagation characteristics are calculated based on the solution. The results are useful in the understanding and design of plate resonators, filters and acoustic wave sensors of ZnO, AlN and polarized ceramics.     

VIBRATION CONFINEMENT OF THICKNESS-SHEAR AND THICKNESS-TWIST MODES IN A FUNCTIONALLY GRADED PIEZOELECTRIC PLATE

We analyze shear-horizontal vibrations of a functionally graded piezoelectric plate of polarized ceramics or crystals of 6mm symmetry.The material of the central portion of the plate is different from that of the rest of the plate.It is shown that when the material properties of the central portion and the rest of the plate satisfy certain conditions,there exist trapped thicknessshear and thickness-twist modes whose vibrations are mainly confined within the central portion and decay quickly outside the central portion.The effects of the functionally graded material properties on the behaviors of the trapped modes are examined.     

Rotation sensitivity of waves propagating in a rotating piezoelectric plate

The rotation effect on the characteristics of waves propagating in a piezoelectric plate is studied in the framework of linear piezoelectricity including Coriolis and centrifugal forces. The rotation sensitivity of the wave dispersion relations is analyzed in details for polarized ceramic plates and for the lowest thickness-shear and the lowest thickness-twist waves because of the particular importance of these modes for gyroscope applications. The analysis shows that the frequency shifts monotonically with the increasing rotation rate and the rotation sensitivity of long waves is substantially greater than that of short waves. Generally, plates with shorted electrode surfaces have higher rotation sensitivity than plates with free-charge surfaces. For long waves and for small rotation rate relative to the wave frequency, the frequency shifts with rotation rate, linearly for plates with shorted electrode surfaces and nonlinearly with a nearly flat initial tangent for plates with free-charge surfaces. These rotation sensitivity characteristics are of interest for the development of rotation sensors and other piezoelectric devices for which frequency insensitivity to rotation is desired.     

功能梯度压电夹层结构中SH波的传播

研究了功能梯度压电上、下半空间和均匀压电层组成的夹层结构中SH波的传播性能,上、下功能梯度半空间的材料性能沿垂直于界面方向以指数函数形式变化。首先推导了SH传播时电弹场的解析解,然后利用界面条件得到了行列式形式的频散方程。基于推导的频散方程,通过数值算例表明了材料性能梯度变化、压电层厚度和材料组合方式对相速度的影响,结果对功能梯度压电材料在声波器件中的应用有参考价值。     

Effects of SH waves in a functionally graded plate

A computational method is presented to investigate SH waves in functionally graded material (FGM) plates. The FGM plate is first divided into quadratic layer elements (QLEs), in which the material properties are assumed as a quadratic function in the thickness direction. A general solution for the equation of motion governing the QLE has been derived. The general solution is then used together with the boundary and continuity conditions to obtain the displacement and stress in the wave number domain for an arbitrary FGM plate. The displacements and stresses in the frequency domain and time domain are obtained using inverse Fourier integration. Furthermore, a simple integral technique is also proposed for evaluating modified Bessel functions with complex valued order. Numerical examples are presented to demonstrate this numerical technique for SH waves propagating in FGM plates.     

AN EXACT ANALYSIS OF FORCED THICKNESS-TWIST VIBRATIONS OF MULTI-LAYERED PIEZOELECTRIC PLATES

This paper deals with the thickness-twist vibration of a multi-layered rectangular piezoelectric plate of crystals of 6 mm symmetry or polarized ceramics.An exact solution is obtained from the three-dimensional equations of linear piezoelectricity.The solution is useful to the understanding and design of composite piezoelectric devices.A piezoelectric resonator,a piezoelectric transformer,and a piezoelectric generator are analyzed as examples.     

ELECTRICALLY FORCED VIBRATION OF A THICKNESS-TWIST MODE PIEZOELECTRIC RESONATOR WITH NON-UNIFORM ELECTRODES

We study the effect of electrodes with varying thickness on thickness-twist vibration of a piezoelectric plate resonator of crystals of 6 mm symmetry.An exact theoretical analysis is performed.Results show that non-uniform electrodes have a strong effect on mode shapes,and suggest the possibility of using nonuniform electrodes for strong energy trapping.     

Coupled extension and thickness-twist vibrations of lateral field excited AT-cut quartz plates简

In this paper, the coupled extension and thickness- twist vibrations are studied for AT-cut quartz plates under Lateral Field Excitation （LFE） with variations along the x1- direction. Mindlin＇s two-dimensional equations are used for anisotropic crystal plates. Both free and electrically forced vibrations are considered. Important vibration characteristics are obtained, including dispersion relations, frequency spectra, and motional capacitances. It is shown that, to avoid the effects of the couplings between extension and thickness-twist vibrations, a series of discrete values of the length/thickness ratio of the crystal plate need to be excluded. The results are of fundamental significance for the design of LFE resonators and sensors.