广义场作用对电磁弹性结构中弹性波传播的影响
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摘要
电磁弹性结构中声表面波的传播特性研究是近年来较新的课题,人们也进行了不断的探索与研究。但对广义场下的情形研究较少,且不系统,特别是电场及磁场下的研究更少。鉴于此,本文将系统的研究广义场下电磁弹性结构中声表面波的传播性能。
从基础理论出发,给出横观各向同性电磁弹性介质的力学、电学和磁学基本方程,得出位移、电势和磁势的一般解,并给出无外加场量下电磁弹性结构中声表面波传播的频散方程。在确定广义场量(磁场、电场、应力)下电磁弹性板中耦合初始广义应力(弹性应力、电位移及磁感应强度)的基础上,根据基本方程,通过势函数法与子波技术相结合的方法,得出广义场量下声表面波的传播特性,并分别给出对称模态和反对称模态时的频散方程——波传播速度与波数的关系。
最后以由BaTiO_3-CoFe_2O_4材料构成的电磁弹性板模型作为数值算例,结合广义场下电磁弹性结构中表面波的频散方程,借助Matlab软件,绘制了电磁弹性结构中Lamb波传播的对称模态及反对称模态频散曲线,并与无外加场量的情况进行对比。计算结果表明,整体而言广义场对声表面波的传播速度有所改变。在外加电场及磁场下的改变量可达2%-5%,特别是在波数(?)＞10,波速改变更加明显,但是所加电场及磁场比较大。在波数(?)＞10时,电场及磁场对波速的改变不太明显。而对于压力作用下的情形,波速的改变较为稳定,其改变幅度不随波数的改变而改变。
The research of propagating characteristics of surface acoustic wave in magneto-electro-elastic structure has been increasingly concerned these days and more and more people are doing related work on the subjects. However, the relevant research of generalized field is rare and unsystematic, especially the research of circumstance in generalized field and magnetic field. So this paper will describe some systematic research on propagating characteristics of surface acoustic wave under generalized field.
On the basis of some basic theories and the macroscopic fundamental equation of mechanical , electrical, magnetical quotations relevant to the transversely isotropic medium and dispersive equation of the surface acoustic wave in magneto-electro-elastic structure, we can get the general solution of displacement electric, potential and magnetic potential. Coupled with initial generalized stress of magneto-electro-elastic plate under generalized field, we can get propagating characteristics of the surface acoustic wave through potential function methods and wavelet techniques, which is the relationship between wave number and the velocity of waves(the dispersive quotation including symmetric modes and anti-symmetric modes)
Finally, Numerical calculations were carried out for a BaTiO_3-CoFe_2O_4 magneto-electro-elastic plate. With the aid of Matlab, we get the symmetric modes and anti-symmetric curves of Lamb wave propagating in magneto-electro-elastic structure, and compared the results to circumstance where there is no field. In general, the result shows that generalized field has effect on the phase velocity of Lamb wave. In the absence of electric field and magnetic field, the phase velocity is changed by 2 to 5 percent, and it is remarkably changed especially when k is more than 10. While k is less than 10, the phase velocity is not changed obviously. However, the electric field and magnetic field must be strong enough. We also find that the velocity changed stably under pressure and its amplitude of variation did not change with the wave number.
从基础理论出发,给出横观各向同性电磁弹性介质的力学、电学和磁学基本方程,得出位移、电势和磁势的一般解,并给出无外加场量下电磁弹性结构中声表面波传播的频散方程。在确定广义场量(磁场、电场、应力)下电磁弹性板中耦合初始广义应力(弹性应力、电位移及磁感应强度)的基础上,根据基本方程,通过势函数法与子波技术相结合的方法,得出广义场量下声表面波的传播特性,并分别给出对称模态和反对称模态时的频散方程——波传播速度与波数的关系。
最后以由BaTiO_3-CoFe_2O_4材料构成的电磁弹性板模型作为数值算例,结合广义场下电磁弹性结构中表面波的频散方程,借助Matlab软件,绘制了电磁弹性结构中Lamb波传播的对称模态及反对称模态频散曲线,并与无外加场量的情况进行对比。计算结果表明,整体而言广义场对声表面波的传播速度有所改变。在外加电场及磁场下的改变量可达2%-5%,特别是在波数(?)＞10,波速改变更加明显,但是所加电场及磁场比较大。在波数(?)＞10时,电场及磁场对波速的改变不太明显。而对于压力作用下的情形,波速的改变较为稳定,其改变幅度不随波数的改变而改变。
The research of propagating characteristics of surface acoustic wave in magneto-electro-elastic structure has been increasingly concerned these days and more and more people are doing related work on the subjects. However, the relevant research of generalized field is rare and unsystematic, especially the research of circumstance in generalized field and magnetic field. So this paper will describe some systematic research on propagating characteristics of surface acoustic wave under generalized field.
On the basis of some basic theories and the macroscopic fundamental equation of mechanical , electrical, magnetical quotations relevant to the transversely isotropic medium and dispersive equation of the surface acoustic wave in magneto-electro-elastic structure, we can get the general solution of displacement electric, potential and magnetic potential. Coupled with initial generalized stress of magneto-electro-elastic plate under generalized field, we can get propagating characteristics of the surface acoustic wave through potential function methods and wavelet techniques, which is the relationship between wave number and the velocity of waves(the dispersive quotation including symmetric modes and anti-symmetric modes)
Finally, Numerical calculations were carried out for a BaTiO_3-CoFe_2O_4 magneto-electro-elastic plate. With the aid of Matlab, we get the symmetric modes and anti-symmetric curves of Lamb wave propagating in magneto-electro-elastic structure, and compared the results to circumstance where there is no field. In general, the result shows that generalized field has effect on the phase velocity of Lamb wave. In the absence of electric field and magnetic field, the phase velocity is changed by 2 to 5 percent, and it is remarkably changed especially when k is more than 10. While k is less than 10, the phase velocity is not changed obviously. However, the electric field and magnetic field must be strong enough. We also find that the velocity changed stably under pressure and its amplitude of variation did not change with the wave number.
引文
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[2]于福熹.信息材料[M].天津:天津大学出版社,2000,P200-222.
[3]吴人洁.复合材料[M].天津:天津大学出版社,2000,P151-158,166-177.
[4]K.K.Patankar,S.A.Patil,K.V.Sivakumar,Y.D.Kolekar,and M.B.Kothale,Mat.Chem.Phys.2000,65:97
[5]Ryu J,Carazo A V.Magnet-electric Properties Piezoelectric-Magnetostrictive Laminate Composites.Jpn.J.Appl.Phys.2001,40:4948.
[6]Van Suchtelen J.Product Properties:A new application of composite materials.Philips Res Rapt,1972,27:28-37.
[7]Boomgaard V D,Born R A.Sintered magnet-electric composite material Ni(Co,Mn) Fe_2O_4.Materials Science & Engineering,1978,13:1538.
[8]Cai N,Zhai J,Nan C W,et al.Dielectric ferroelectric magnetic and magnetoelectric properties of multiferroic laminated composites Physics Review B.2003,68:224.
[9]Ryu Jungho,Priya Shashank.Effect of the Magnetostrictive Layer on Magnetoelectric Properties in Lead Zirconate Titanate/Terfenol D Laninate Composites.Journal of the American Ceramic Society.2001,84(12):2095.
[10]G.Engdahl.Handbook of Giant Magnetostfictive Materials Academic Press,San Diego CA,2000:127.
[11]Ryu Jungho,Alfredo Vazquez Carazo,Uchino Kenji et al.Piezoelectric and Magnet-electric Properties of Lead Zirconate Titanate/Ni-Ferrite Particulate Composites.Electric- overamics.2000,7:17-24.
[12]Wan J G.Liu J M.Giant magnet-electric effect of a hybrid of Magnetostric and Piezoelectric composites.J.Appl.Phys.2003 93(12):9916.
[13]万红,吴学忠,刘希从.层状复合材料磁电效应的数值分析.功能材料.2005,36(4):509-512.
[14]Harshe G.Dougherty J P and Newnham R E.Theoretical modeling of multilayer magnet-electric composites.International Journal of Applied Electromagnetic in materials,1993,4:145-159.
[15]Avellaneda M,Harshe G.Magnetoelectfic effect in Piezoelectric/ Magnetostrictive multilayer(2-2)composites.Journal of Intelligent Material Systems and Structures,1994,5(4):501-513.
[16]Nan C W.Magnetoelectric effect in composites of Piezoelectric and Piezomagnetic Phases.Physical ReviewB,1994,50(9):6082-6088.
[17]Benveniste J.Magnetoelectric effect in fibrous composites of Piezoelectric and Piezomagnetic Phases Physical Review B,1995,51(22):16424-16427.
[18]Huang J H,Liu H K,Dai W H.The optimized fiber volume fraction for magnetoelectric coupling effect in piezoelectric-piezomagnetic continuous fiber reinforced composites.International Journal of Engineering Science,2000,38(11):1207-1271.
[19]Ryu Jungho,Priya Shashank,Uchino Kenji,et al.Magnetoelectric effect in the composites of Magnetostrictive and piezoelectric materials.Journal of Electro ceramics,2002,8(2):107-119.
[20]Wang X M,Shen Y P.The conservation laws and path-independent integrals with an application for linear electro-magneto-elastic media.International Journal of Solids and Structures,1996,33(6):865-878.
[21]Li J Y,Dunn M L.Micromechanics of magnetoelectroelastic composite materials:average fields and effective behaviors.Journal of Intelligent Material Systems and structures,1998,9(6):404-416.
[22]Pan E.Exact solution for simply supported and multilayered magneto-electro-elastic plates.Journal of Applied Mechanics,2001,68(6):608-618.
[23]Pan E,Heyliger P R.Free vibrations of simply supported and multilayered magneto-electro-elastic plates.Journal of Sound and Vibrations,2002,252(3):429-442.
[24]Pan E,Heyliger P R.Exact solutions for magneto-electro-elastic laminates in cylindrical bending.International Journal of Solids and Structures,2003,40(24):6859-6876.
[25]Pan E,Han F.Exact solutions for functionally graded and layered magneto-electro-elastic plates.International Journal of Engineering Science,2005,43(3-4):321-339.
[26]Wang X,Shen Y P.The general solution of the three-dimensional problems in magnetoelectroelastic media.International Journal of Engineering Science,2002,40(10):1069-1080.
[27]刘金喜,王祥琴,王彪.横观各向同性电磁弹性固体耦合方程的一般解.应用数学和力学,2003,24(7):684-690.
[28]Wang X,Zhong Z,The general solution of spherically isotropic magnetoelectroelastic media and its applications.European Journal of Mechanics A/Solids,2003,22(6):953-969.
[29]丁皓江,陈江瑛,侯鹏飞.磁电弹性圆锥顶端作用集中荷载的解析解.力学季刊,2003,24(3):292-298.
[30]陈江瑛,丁皓江,侯鹏飞.磁电弹性旋转圆环(圆盘)的三维分析.浙江大学学报,2003,37(4):440-444.
[31]Wang X,Zhong Z.A finitely long circular cylindrical shell of piezoelectric piezomagnetic composite under pressuring and temperature change.International Journal of Engineering Science,2003,41(18):2143 -2159
[32]关群,何顺荣.压电、压磁弹性体平面问题的通解.上海交通大学学报,2004,38(8):1417-1422.
[33]Guan Q,He S R.Two-dimensional analysis of piezoelectric/piezomagnetic and elastic media.Composite Structures,2005,69(2):229-237.
[34]关群,何顺荣.压电、压磁弹性体的空间问题研究.哈尔滨工业大学学报,2005,37(5):709-712.
[35]关群,何顺荣.压电、压磁耦合弹性介质圆板的自由振动.哈尔滨工业大学学报,2005,37(3):418-422.
[36]江爱民,林定远,邱洪林.均布荷载作用下悬臂磁电弹性梁的解析解.应用力学学报,2004,21(4):106-109.
[37]江爱民,邱洪林,林定远.均布荷载作用下简支磁电弹性梁的解析解.浙江工业大学学报,2004,32(2):239-244.
[38]卿光辉,邱家俊,刘艳红.磁电弹性体修正后的H-R混合变分原理和状态向量方程.应用数学和力学,2005,26(6):665-670.
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