PMN-PT夹层弹性半空间结构中SH波的传播

分析了弹性上下半空间和PMN-PT单晶层组成的夹层结构中SH波的传播性质,PMN-PT单晶沿[011]c方向极化,宏观上呈mm2对称,且晶体沿角度θ方向切割。基于正交各向异性压电材料和各向同性弹性材料的基本方程,得到了夹层结构中SH波传播时行列式形式的频散方程。通过对数值算例进行分析可以看出,PMN-PT单晶的切割角度和弹性材料属性对结构中的相速度有很大影响,因此波的某些传播性能可以通过材料的设计以及晶体切割的方向来实现,这些结论为声表面波器件的开发和应用提供了理论依据。     

具有表面效应的压电半空间中的表面波

纳米科技的快速发展使压电纳米结构在纳米机电系统中得到广泛应用,形成了诸如纳米压电电子学等新的研究方向.与传统的宏观压电材料相比,在纳米尺度下压电材料往往呈现出不同的力学特性,而造成这种差异的原因之一便是表面效应.本文基于Stroh公式、Barnett-Lothe积分矩阵及表面阻抗矩阵,研究计入表面效应的任意各向异性压电半空间中的表面波传播问题,导出了频散方程.针对横观各向同性压电材料,假设矢状平面平行于材料各向同性面,发现Rayleigh表面波和B-G波解耦,并得到各自的显式频散方程.结果表明,Rayleigh表面波的波速小于偏振方向垂直于表面的体波,而B-G波的波速小于偏振方向垂直于矢状平面的体波.以PZT-5H材料为例,用数值方法考察表面残余应力和电学边界条件对表面波频散特性的影响发现:表面残余应力只对第一阶Rayleigh波有明显的影响;电学开路情形的B-G波比电学闭路情形的B-G波传播快.本文工作可为纳米表面声波器件的设计或压电纳米结构的无损检测提供理论依据.     

PMN-PT夹层弹性半空间结构中SH波的传播Propagation of SH waves in sandwich structures consisting of PMN-PT single crystal layer and elastic half-spaces

分析了弹性上下半空间和PMN‐PT单晶层组成的夹层结构中SH波的传播性质,PMN‐PT单晶沿[011]c方向极化,宏观上呈mm2对称,且晶体沿角度θ方向切割。基于正交各向异性压电材料和各向同性弹性材料的基本方程,得到了夹层结构中SH波传播时行列式形式的频散方程。通过对数值算例进行分析可以看出,PMN‐PT单晶的切割角度和弹性材料属性对结构中的相速度有很大影响,因此波的某些传播性能可以通过材料的设计以及晶体切割的方向来实现,这些结论为声表面波器件的开发和应用提供了理论依据。     

弱界面压电／压磁层状结构中的SH波

研究了弱界面压电层/压磁半空间结构中SH波的频散特性, 界面性能由 ``弹簧'模型表征, 压电层的表面考虑电学短路和电学开路两种边界条件. 推导了显函形式的 频散方程, 并结合算例分析了界面性能和电学边界条件对SH波传播特性的影响. 数值结果表 明: 弱界面降低了SH波传播的相速度; 对于短路电边界条件, 弱界面可以使一阶模态的相速 度小于B-G表面波的速度; 对于开路电边界条件, 一阶模态的相速度总是大于剪切体波的波 速.     

非理想界面弹性层/压电柱结构中SH波的传播特性

研究了各向同性弹性层与压电柱之间非理想连接时沿周向传播的SH波的频散特性.弹性层表面力学自由;弹性层与压电柱之间应力连续、位移间断.通过求解控制方程,将问题的解用Bessel函数表示,利用界面条件和边界条件得到频散方程,然后对其进行数值求解,分析了界面性态、材料常数和几何尺寸对SH波传播特性的影响.     

非均匀压电层状结构中Love波的传播

讨论材料参数沿厚度方向发生连续缓慢变化时的各向同性弹性基底上有一等厚压电覆盖层肘Love波的传播性能．给出了压电层的厚度和基底材料的非均匀性对频散曲线的影响．     

多层电磁弹性圆柱壳内波的轴向传播

对多层电磁弹性圆柱壳内波的轴向传播进行了分析。根据柱坐标系下电磁弹性多层结构的几何方程、平衡方程和本构方程,推导出了两个层间变量所满足的状态方程。通过状态方程的解和层间变量连续性条件,得到了多层圆柱体内外表面层间变量的传递关系。最后利用边界条件,导出了波在传播时所满足的频散方程,并求得该结构的模态参数。以一个三层的压电/压磁材料组成的柱壳结构作为数值算例,计算出波在其中轴向传播时的频散关系和模态参数,并对计算结果进行了分析。     

基于带状单元法的电磁弹性多层板复频散特性分析

超声波在弹性介质中传播时理论上可以分为传播、非传播及衰减模式,且分别与实、虚及复波数相对应,可用复频散特性来进行描述.这一性质在电磁弹性多层板结构中同样存在.该文利用带状单元法对其进行了分析和计算.首先,利用能量守恒定律并结合介质的本构方程、平衡方程及相应边界条件构建了结构的带状单元模型,然后利用该模型获得了电磁弹性多层板的频散方程,最后以一个由压电材料BaTiO3和压磁材料CoFe2O4构成的三层板为数值分析对象,给出了波在其中传播时的复频散特性,并利用计算结果证明了当前相关文献中材料常数引用的不合理性.     

覆盖层与基底极化方向相反时压电层状半空间中的B-G波

对于覆盖层与基底介质极化方向相反的压电状半空间,在自由表面电学开路和短路两种情况下,分析用解析的方法以了Ｂｌｅｕｓｔｅｉｎ－Ｇｕｌｙａｅｖ波传播的相速度方程或相速度的表达式;以工程技术中应用的压电材料为例考察了波速随覆盖厚度ｈ的变化规律,为了分析表面金属薄膜对波的传播速度的影响,计算了机电耦合系数ｋ＾２与ｈ的关系,结果表明：层状结构Ｂ－Ｇ波传播时具有很小的穿透深度,同时在ｈ取适当值时依然可使ｋ＾２     

压电空心圆柱中的波特性

基于三维线性压电弹性理论,采用Legendre多项式方法研究了电开路时压电空心圆柱中轴向波的传播特性.给出了结构的频散曲线及其相应的非压电情况,展示了压电的影响.比较了压电对轴对称模态和弯曲模态影响的区别.从电势分布的角度分析了压电对弯曲扭转波的影响.最后讨论了径厚比和极化方向对波传播压电效应的影响.     

Propagation behavior of SH waves in a piezomagnetic substrate with an orthorhombic piezoelectric layer

The dispersion behavior of the shear horizontal (SH) waves in the coupled structure consisting of a piezomagnetic substrate and an orthorhombic piezoelectric layer is investigated with different cut orientations. The surface of the piezoelectric layer is mechanically free, electrically shorted, or open, while the surface of the piezomagnetic substrate is mechanically free, magnetically open, or shorted. The dispersion relations are derived for four electromagnetic boundary conditions. The dispersion characteristics are graphically illustrated for the layered structure with the PMN-PT layer perfectly bonded on the CoFe₂O₄ substrate. The effects of the PMN-PT cut orientations, the electromagnetic boundary conditions, and the thickness ratio of the layer to the substrate on the dispersion behavior are analyzed and discussed in detail. The results show that, (i) the effect of the cut orientation on the dispersion curves is very obvious, (ii) the electrical boundary conditions of the PMN-PT layer dominate the propagation feature of the SH waves, and (iii) the thickness ratio has a significant effect on the phase velocity when the wave number is small. The results of the present paper can provide valuable theoretical references to the applications of piezoelectric/piezomagnectic structure in acoustic wave devices.     

Love waves in a two-layered piezoelectric/elastic composite plate with an imperfect interface

Based on the shear spring model, the propagation of Love wave in two-layered piezoelectric/elastic composite plates under the influence of interfacial defect is investigated. The piezoelectric layer is electrically shorted at both top and bottom surfaces. The wave form solutions of the piezoelectric and elastic layers are obtained, and the dispersion equation is derived by subjecting the boundary conditions and the continuity conditions to the obtained wave form solutions. Numerical results are performed for PZT4/aluminum composite plate. The phase velocities and the mode shapes of mechanical displacement and electric potential are illustrated graphically. The results show that both the interfacial defect and the thickness ratio between the piezoelectric and elastic layers have significant effect on the propagation characteristics of Love wave. One important feature is observed that the interfacial defect always decreases the phase velocities.     

Love waves in functionally graded piezoelectric materials

To investigate the features of Love waves in a layered functionally graded piezoelectric structure, the mathematical model is established on the basis of the elastic wave theory, and the WKB method is applied to solve the coupled electromechanical field differential equation. The solutions of the mechanical displacement and electrical potential function are obtained for the piezoelectric layer and elastic substrate. The dispersion relations of Love waves are deduced for electric open and short cases on the free surface respectively. The actual piezoelectric layer–elastic substrate systems are taken into account, and some corresponding numerical examples are proposed comparatively. Thus, the effects of the gradient variation about material constants on the phase velocity, the group velocity, the coupled electromechanical factor and the cutoff frequency are discussed in detail. So the propagation behaviors of Love waves in inhomogeneous medium is revealed, and the dispersion and the anti-dispersion are analyzed. The conclusions are significant both theoretically and practically for the surface acoustic wave devices.     

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。     

初应力对压电层状结构声表面波传播性能的影响

研究了压电层状结构中初应力对广义Ｒａｙｌｅｉｇｈ波传播相速度和机电耦合性能的影响,通过求解含初应力的运动微分方程,对自由界面电学开路和短路两种情况得到了相应的相速度方程。给出了具体的数值算例,所得结果对于提高和改善声表面波器件性能有参考意义。     

压电空心圆柱中波的传播

应用三维压电弹性体轴对称模型对压电空心圆柱中波的传播进行了研究. 发现在 圆柱中是否具有压电性质会对波的传播带来显著的差异. 当波长趋向于零时，在压电圆柱中 拟P波的波速渐进趋向于横观各向同性弹性体的准P波波速，而非压电圆柱中拟P波的波速 渐进趋向于一维杆模型中的P波波速；在压电圆柱中拟SV波存在驻波现象. 圆柱中的SH波 同电场无关，所以在压电圆柱和非压电圆柱中SH波具有相同的频散曲线. 应用积分变 换方法将圆柱的控制方程同其侧边界条件相结合，得到了一组动力学方程. 针对具体的侧边 界条件，得到相对应的波导条件和频散方程. 在此基础上通过数值计算模拟了圆柱受到端部 应力脉冲激励后的瞬态响应. 同时讨论了空心圆柱的半径比对轴向波传播的影响.     

On diffraction of acoustic and electric waves in piezoelectric medium by an absorbent half-plane electrode

Diffraction of incident acoustic and incident electric waves in a transversally isotropic piezoelectric medium at the boundary of a half-plane absorbent electrode is systematically investigated using the quasi-hyperbolic approximation. The electrode is assumed to be very thin so that its thickness and stiffness can be neglected. By exact inversion, the explicit expressions for the scattering waves are obtained. A closed form solution is obtained by applying Laplace transformations and the Wiener–Hopf technique. By means of the Cagniard–de Hoop method a detailed investigation of the structure of the electro-acoustic wave is conducted. The mode conversion between electric and acoustic waves, the effect of electro-acoustic head wave, the Bleustein–Gulyaev surface wave and the structure of the wave in terms of the type of the incident wave (acoustic or electric) and its angle of incidence are analyzed in detail. It is shown that in piezoelectric materials, absorbent electrodes are neither completely opaque nor completely transparent to electric and acoustic waves. The dynamic field intensity factors at the tip of the electrode are functions of the angle of incidence and time; they are derived explicitly and discussed through a detailed numerical analysis.