层状磁电复合材料中弹性波传播若干问题的理论研究
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摘要
磁电复合材料是由压电材料和压磁材料按照一定的方式复合而成的新型功能材料,这类材料能实现机械能、电能和磁能之间的相互转换。其磁—电—力的多场耦合效应使其成为制作传感器、磁电控制装置、微波器件和其它电子产品的首选材料,在信号处理、自动控制、微波通讯和新兴智能材料系统与结构等领域显示出诱人的应用前景。由压电材料和压磁材料交替叠合而成的压电/压磁层状复合材料或结构是各种电磁元器件的基本构成形式,其中许多可能的应用与弹性波的传播问题密切相关,因此本文将对横观各向同性压电/压磁层状复合材料或结构中若干基本的波动问题进行研究,主要内容有:
1)弹性波在压电/压磁材料界面上的反射和折射。考虑了准纵波(QP波)和准横波(QSV波)分别从压电介质和压磁介质单独入射时各散射体波的反射、折射系数以及能量系数随入射角的变化规律,讨论了波型转换以及入射波在界面上的能量转换和分配。研究结果表明:反射和折射场有6种散射波,即耦合的QP波、QSV波,耦合的凋落声电波(EA波)、凋落声磁波(MA波),以及与弹性位移解耦的凋落电势波(EP波)和磁势波(MP波)。绝大部分的入射波能量由与入射波相同类型的波所携带,波型转换生成的波只占有很少一部分能量。
2)压电/压磁覆层半空间结构中Rayleigh型表面波的传播.考查了压电覆层自由表面4种不同的电磁学边界条件以及压电覆层的材料特性对频散曲线和模态分布的影响。研究表明:结构频散特性和模态分布主要受压电层表面的电学条件影响,磁学条件主要影响最低阶模态。压电材料的剪切体波波速越大,相应的覆层半空间结构中波的传播速度也就越大。
3)弹性波沿压电/压磁周期层状结构中铺层方向的传播。讨论了不同的压电相体积份数以及压电材料特性对频散曲线和模态分布的影响。结果表明:复合结构的频散曲线类似于自由板中Lamb波的对称模态,每条连续的频散曲线并不代表一个单一的振动模态。相邻两阶模态的频散曲线间存在着交叉点,在交叉点附近发生波模态转换现象。
4)压电/压磁周期层状结构中弹性波的传播和局部化特性。考虑了弹性波垂直传播和倾斜传播的情况。采用传递矩阵法和/或刚度矩阵法计算了频散曲线、局部化因子和响应频谱等参量,分析了弹性波在周期结构中的传播特性。研究结果表明:由频散曲线、透射波的频率响应以及局部化因子这三个表征参数所描述的频带结构特征是一致的。弹性波沿结构的周期方向传播时存在频率通带和频率禁带,其带隙的大小取决于结构组分材料的弹性常数差值,其差值越大,则带隙频率范围越宽;不论QP波还是QSV波斜传播,在通带频率范围内,与入射波同类型的透射波强度总是最大;而在某些通带频率下,波型转换生成的QSV或QP波的透射系数也会达到很大;相比于力电耦合的透射EA波和力磁耦合的透射MA波,透射MP波与EP波的强度稍大。
特别值得指出的是,与以往大多数研究工作不同,本文采用了考虑磁势的压电材料本构方程与考虑电势的压磁材料本构方程来求解具体的波动问题,这样既符合实际压电/压磁层状复合材料的结构特点,在数学上又精确满足了压电/压磁界面的连续性条件,而且在物理上带来一些新的波型。本文的工作不仅完善了磁电复合材料的波动理论,而且对磁电复合材料器件的分析和设计具有重要的理论指导意义。
Magnetoelectric(ME) composites or structures consisting of piezoelectric(PE) and piezomagnetic(PM) materials are a new kind of functionally materials,which can facilitate the conversion among mechanical,electric and magnetic energies.Due to the magnetic-electric-mechanical coupling effect,ME composites are potential candidates for use as sensors,ME control components,microwave devices as well as other electric products,which makes them ready for technological application in the fields of signal processing,self-control,microwave communication and newly intelligence material systems and structures.The ME layered composites or structures consisting of alternative layered PE and PM materials are basic configurations for magnetic-electric devices.A lot of possible applications are associated with wave propagation problems in such composites.Thus,several basic problems for wave propagation in layered transversely isotropic ME composites or structures are investigated in this dissertation. The main contents are as follows.
1) Reflection and refraction of plane waves at the interface between PE and PM media are studied.The reflection and refraction coefficients and energy coefficients varying with the incident angle are examined for quasi-longitudinal(QP) and quasi-transverse(QSV) waves incidence from PE or PM media.The wave mode conversion and the energy conservation and partition at the interface are discussed. The results show that the reflected and refracted wave fields consist of six different mode,i.e.the coupled QP and QSV waves,evanescent electroacoustic(EA) and magnetoacoustic(MA) waves,the uncoupled magnetic potential(MP) and electric potential(EP) waves.The most amount of the incident wave energy is carried by the waves that are of the same mode as the incident wave,while the energy arising from wave mode conversion occupies a less part of the incident energy.
2) The Rayleigh-type surface wave propagation in a piezoelectric layer over a piezomagnetic half-space is investigated.The effects of four different kinds of electric-magnetic boundary conditions on the dispersion curves and mode shapes of displacements,electric and magnetic potentials are discussed.The results show that the electric boundary conditions dominate the phase velocity and mode shapes for the second mode and that the magnetic boundary conditions have a significant effect on the first mode.The larger the shear velocity of the piezoelectric layer is and the larger the phase velocity of Rayleigh-type surface wave is.
3) Wave propagation along the interface in PE/PM layered periodic composites is studied.The effects of the different piezoelectric volume fraction and the properties of piezoelectric layer on the dispersion curves and the mode shapes of displacement, electric and magnetic potentials are discussed.The results show that the dispersion curves resemble the symmetric Lamb waves in a plate.Each continuous curve does not necessarily represent a single mode.Wave mode exchange takes place at the crossover point between dispersion curves of the adjoining two branches.
4) Wave propagation and localization in periodic layered PE/PM structures are studied, considering two cases of wave propagation in both normal and oblique directions. Wave behaviors are analyzed by calculating the dispersion curves,localization factors and response spectra by using the transfer matrix and/or the stiffness matrix methods.The results show that the band structures are described consistently by the dispersion curves,the localization factors and the response spectra of the transmitted waves.The frequency passbands and stopbands exist in the PE/PM periodic layered structures.The width of the gaps is determined by the differences between material constants of each constituent in PE/PM composites.The bigger the difference is,the wider the gap is.The most energy is carried by the transmitted waves which are of the same mode as the incident wave when the frequencies are at the passbands.However,the transmitted coefficients of QSV or QP waves arising from wave mode conversion may be very large at some particular frequencies in some passbands.Compared to the coupled transmitted MA and EA waves,the transmitted coefficients of EP and MP waves are a little bigger.
It is worth mentioning that,unlike the published works,the present dissertation has solved wave propagation problems in the layered PE/PM composites by considering magnetic potential in the PE material constitutive equations and electric potential in the PM material constitutive equations.This,we believe,not only is consistent to the actual PE/PM layered structure characteristics,but also satifies the continuity conditions accurately at the interface of the PE and PM materials from the point of view of the mathematics.Further,the new wave modes come into being physically.The investigation not only enriches the elastic wave theory of the ME composites,but also serves theoretical guide in the analysis and design of ME devices.
1)弹性波在压电/压磁材料界面上的反射和折射。考虑了准纵波(QP波)和准横波(QSV波)分别从压电介质和压磁介质单独入射时各散射体波的反射、折射系数以及能量系数随入射角的变化规律,讨论了波型转换以及入射波在界面上的能量转换和分配。研究结果表明:反射和折射场有6种散射波,即耦合的QP波、QSV波,耦合的凋落声电波(EA波)、凋落声磁波(MA波),以及与弹性位移解耦的凋落电势波(EP波)和磁势波(MP波)。绝大部分的入射波能量由与入射波相同类型的波所携带,波型转换生成的波只占有很少一部分能量。
2)压电/压磁覆层半空间结构中Rayleigh型表面波的传播.考查了压电覆层自由表面4种不同的电磁学边界条件以及压电覆层的材料特性对频散曲线和模态分布的影响。研究表明:结构频散特性和模态分布主要受压电层表面的电学条件影响,磁学条件主要影响最低阶模态。压电材料的剪切体波波速越大,相应的覆层半空间结构中波的传播速度也就越大。
3)弹性波沿压电/压磁周期层状结构中铺层方向的传播。讨论了不同的压电相体积份数以及压电材料特性对频散曲线和模态分布的影响。结果表明:复合结构的频散曲线类似于自由板中Lamb波的对称模态,每条连续的频散曲线并不代表一个单一的振动模态。相邻两阶模态的频散曲线间存在着交叉点,在交叉点附近发生波模态转换现象。
4)压电/压磁周期层状结构中弹性波的传播和局部化特性。考虑了弹性波垂直传播和倾斜传播的情况。采用传递矩阵法和/或刚度矩阵法计算了频散曲线、局部化因子和响应频谱等参量,分析了弹性波在周期结构中的传播特性。研究结果表明:由频散曲线、透射波的频率响应以及局部化因子这三个表征参数所描述的频带结构特征是一致的。弹性波沿结构的周期方向传播时存在频率通带和频率禁带,其带隙的大小取决于结构组分材料的弹性常数差值,其差值越大,则带隙频率范围越宽;不论QP波还是QSV波斜传播,在通带频率范围内,与入射波同类型的透射波强度总是最大;而在某些通带频率下,波型转换生成的QSV或QP波的透射系数也会达到很大;相比于力电耦合的透射EA波和力磁耦合的透射MA波,透射MP波与EP波的强度稍大。
特别值得指出的是,与以往大多数研究工作不同,本文采用了考虑磁势的压电材料本构方程与考虑电势的压磁材料本构方程来求解具体的波动问题,这样既符合实际压电/压磁层状复合材料的结构特点,在数学上又精确满足了压电/压磁界面的连续性条件,而且在物理上带来一些新的波型。本文的工作不仅完善了磁电复合材料的波动理论,而且对磁电复合材料器件的分析和设计具有重要的理论指导意义。
Magnetoelectric(ME) composites or structures consisting of piezoelectric(PE) and piezomagnetic(PM) materials are a new kind of functionally materials,which can facilitate the conversion among mechanical,electric and magnetic energies.Due to the magnetic-electric-mechanical coupling effect,ME composites are potential candidates for use as sensors,ME control components,microwave devices as well as other electric products,which makes them ready for technological application in the fields of signal processing,self-control,microwave communication and newly intelligence material systems and structures.The ME layered composites or structures consisting of alternative layered PE and PM materials are basic configurations for magnetic-electric devices.A lot of possible applications are associated with wave propagation problems in such composites.Thus,several basic problems for wave propagation in layered transversely isotropic ME composites or structures are investigated in this dissertation. The main contents are as follows.
1) Reflection and refraction of plane waves at the interface between PE and PM media are studied.The reflection and refraction coefficients and energy coefficients varying with the incident angle are examined for quasi-longitudinal(QP) and quasi-transverse(QSV) waves incidence from PE or PM media.The wave mode conversion and the energy conservation and partition at the interface are discussed. The results show that the reflected and refracted wave fields consist of six different mode,i.e.the coupled QP and QSV waves,evanescent electroacoustic(EA) and magnetoacoustic(MA) waves,the uncoupled magnetic potential(MP) and electric potential(EP) waves.The most amount of the incident wave energy is carried by the waves that are of the same mode as the incident wave,while the energy arising from wave mode conversion occupies a less part of the incident energy.
2) The Rayleigh-type surface wave propagation in a piezoelectric layer over a piezomagnetic half-space is investigated.The effects of four different kinds of electric-magnetic boundary conditions on the dispersion curves and mode shapes of displacements,electric and magnetic potentials are discussed.The results show that the electric boundary conditions dominate the phase velocity and mode shapes for the second mode and that the magnetic boundary conditions have a significant effect on the first mode.The larger the shear velocity of the piezoelectric layer is and the larger the phase velocity of Rayleigh-type surface wave is.
3) Wave propagation along the interface in PE/PM layered periodic composites is studied.The effects of the different piezoelectric volume fraction and the properties of piezoelectric layer on the dispersion curves and the mode shapes of displacement, electric and magnetic potentials are discussed.The results show that the dispersion curves resemble the symmetric Lamb waves in a plate.Each continuous curve does not necessarily represent a single mode.Wave mode exchange takes place at the crossover point between dispersion curves of the adjoining two branches.
4) Wave propagation and localization in periodic layered PE/PM structures are studied, considering two cases of wave propagation in both normal and oblique directions. Wave behaviors are analyzed by calculating the dispersion curves,localization factors and response spectra by using the transfer matrix and/or the stiffness matrix methods.The results show that the band structures are described consistently by the dispersion curves,the localization factors and the response spectra of the transmitted waves.The frequency passbands and stopbands exist in the PE/PM periodic layered structures.The width of the gaps is determined by the differences between material constants of each constituent in PE/PM composites.The bigger the difference is,the wider the gap is.The most energy is carried by the transmitted waves which are of the same mode as the incident wave when the frequencies are at the passbands.However,the transmitted coefficients of QSV or QP waves arising from wave mode conversion may be very large at some particular frequencies in some passbands.Compared to the coupled transmitted MA and EA waves,the transmitted coefficients of EP and MP waves are a little bigger.
It is worth mentioning that,unlike the published works,the present dissertation has solved wave propagation problems in the layered PE/PM composites by considering magnetic potential in the PE material constitutive equations and electric potential in the PM material constitutive equations.This,we believe,not only is consistent to the actual PE/PM layered structure characteristics,but also satifies the continuity conditions accurately at the interface of the PE and PM materials from the point of view of the mathematics.Further,the new wave modes come into being physically.The investigation not only enriches the elastic wave theory of the ME composites,but also serves theoretical guide in the analysis and design of ME devices.
引文
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