General Solution for the Coupled Equations of Transversely Isotropic Magnetoelectroelastic Solids

LIU Jin-xi; WANG Xiang-qin; WANG Biao

Volume 24 Issue 7

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 2003 > 24(7): 684-690

LIU Jin-xi, WANG Xiang-qin, WANG Biao. General Solution for the Coupled Equations of Transversely Isotropic Magnetoelectroelastic Solids[J]. Applied Mathematics and Mechanics, 2003, 24(7): 684-690.

Citation:

LIU Jin-xi, WANG Xiang-qin, WANG Biao. General Solution for the Coupled Equations of Transversely Isotropic Magnetoelectroelastic Solids[J]. Applied Mathematics and Mechanics, 2003, 24(7): 684-690.

Citation:

LIU Jin-xi, WANG Xiang-qin, WANG Biao. General Solution for the Coupled Equations of Transversely Isotropic Magnetoelectroelastic Solids[J]. Applied Mathematics and Mechanics, 2003, 24(7): 684-690.

PDF( 298 KB)

General Solution for the Coupled Equations of Transversely Isotropic Magnetoelectroelastic Solids

1.
Department of Mechanics and Engineering Science, Shijiazhuang Railway Institute, Shijiazhuang 050043, P. R. China;
2.
Department of Communication Engineering, Shijiazhuang Railway Institute, Shijiazhuang 050043, P. R. China;
3.
Electro-Optics Technology Center, Harbin Institute of Technology, Harbin 150001, P. R. China

Received Date: 2002-01-17
Rev Recd Date: 2003-03-11
Publish Date: 2003-07-15

Abstract

Abstract

The coupling feature of transversely isotropic magnetoelectroelastic solids are governed by a system of five partial differnetial equations with respect to the elastic displacements,the electric potential and the magnetic potential.Based on the potential theory,the coupled equations are reduced to the five uncoupled generalized Laplace equations with respect to five potential functions.Further,the elastic fields and electromagnetic fields are expressed in terms of the potential functions.These expressions constitute the general solution of transversely isotropic magnetoelectroelastic media.
- magnetoelectroelastic solids,
- general solution,
- potential function

FullText(HTML)

References(18)

References

[1]	Avellaneda M,Harshe G.Magnetoelectric effect in piezoelectric/magnetostrictive multilayer(2-2)composite[J].J Intell Mater Syst Struct,1994,5(4):501-513.
[2]	Alshits V I,Darinskii A N,Lothe J.On the existence of surface waves in half-infinite anisotropic elastic media with piezoelectric and piezomagnetic properties[J].Wave Motion,1992,16(3):265-283.
[3]	Alshits V I,Barnett D M,Darinskii A N,et al.On the existence problem for localized acoustic waves on the interface between two piezocrystals[J].Wave Motion,1994,20(4):233-244.
[4]	Alshits V I,Kirchner K O K,Ting T C T.Angularly inhomogeneous piezoelectric piezomagnetic magnetoelectric anisotropic media[J].Phil Mag Lett,1995,71(5):285-288.
[5]	Chung M Y,Ting T C T.The Green function for a piezoelectric piezomagnetic magnetoelectric anisotropic elastic medium with an elliptic hole or rigid inclusion[J].Phil Mag Lett,1995,72(6):405-510.
[6]	Kirchner H O K,Alshits V I.Ealstically anisotropic angularly inhomogeneous media-Ⅱ:The Green's function for piezoelectric,piezomagnetic and magnetoelectric media[J].Phil Mag,1996,74(4):861-885.
[7]	LIU Jin-xi,LIU X L,Zhao Y B.Green's functions for anisotropic magnetoelectroelastic solids with an elliptical cavity or a crack[J].Int J Engng Sci,2001,39(12):1405-1418.
[8]	Benvensite Y.Magnetoelectric effect in fibrous composites with piezoelectric and piezomagnetic phases[J].Phys Rev B,1994,51(22):16424-16427.
[9]	Huang J H,Kuo W S.The analysis of piezoelectric/piezomagnetic composite materials containing ellipsoidal inclusions[J].J Appl Phys,1997,81(3):1378-1386.
[10]	Huang J H,Chiu Y H,Liu H K.Magneto-electro-elastic Eshelby tensors for a piezoelectric-piezomagnetic composite reinforced by ellipsoidal inclusions[J].J Appl Phys,1998,83(10):5364-5370.
[11]	Huang J H,Liu H K,Dai W L.The Optimized fiber volume fraction for magnetoelectric coupling effect in piezoelectric-piezomagnetic continuous fiber reinforced composites[J].Int J Engng Sci,2000,38(11):1207-1217.
[12]	LI J Y,Dunn M L.Anisotropic coupled-field inclusion and inhomogeneity problems[J].Phil Mag,1998,77(5):1341-1350.
[13]	Li J Y.Magnetoelectroelastic multi-inclusion and inhomogeneity problems and their applications in composite materials[J].Int J Engng Sci,2000,38(18):1993-2011.
[14]	Fabricant V I.Application of Potential Theory in Mechanics[M].Dordrecht:Kluwer Academic Publishers,1989.
[15]	Wang Z K,Zheng B L.The general Solution of three-dimensional problems in piezoelectric media[J].Int J Solids Strut,1995,32(11):105-115.
[16]	Podil'chuk Y N.Representation of the general solution of static equations of the electroelasticity of a transversely isotropic piezoceramic body in terms of harmonic function[J].Int A ppl Mech,1998,34(7):623-628.
[17]	Chen W Q.On the application of potential theory in piezoelectricity[J].J Appl Mech,1996,66(3):808-811.
[18]	Karapetian E,Sevostianov I,Kachanov M.Point force and point electric charge in infinite and semiinfinite transversely isotropic piezoelectric solids[J].Phil Mag B,2000,80(3):331-359.

Relative Articles

[1]	SUN Jialiang, ZHANG Xiaoliang, JIN Dongping. Separation and Reconfiguration Dynamics of Stacked Satellites[J]. Applied Mathematics and Mechanics, 2024, 45(1): 1-11. doi: 10.21656/1000-0887.440222
[2]	Eburilitu, Alatancang. Eigenfunction Expansion Method of Upper Triangular Operator Matrix and Application to Two-Dimensional Elasticity Problems Based on Stress Formulation[J]. Applied Mathematics and Mechanics, 2012, 33(2): 221-230. doi: 10.3879/j.issn.1000-0887.2012.02.007
[3]	HUANG Jun-jie, Alatancang, WANG Hua. Eigenfunction Expansion Method and Its Application to Two-Dimensional Elasticity Problems Based on Stress Formulation[J]. Applied Mathematics and Mechanics, 2010, 31(8): 992-1000. doi: 10.3879/j.issn.1000-0887.2010.08.012
[4]	ZHOU Hong-yan, PIAO Da-xiong. Hamiltonian Long Wave Expansions for Internal Waves Over a Periodically Varying Bottom[J]. Applied Mathematics and Mechanics, 2008, 29(6): 676-686.
[5]	BIAN Wen-feng, WANG Biao. Dual Equations and Solutions of Ⅰ-Type Crack of Dynamic Problems in Piezoelectric Materials[J]. Applied Mathematics and Mechanics, 2007, 28(6): 651-658.
[6]	YAO Wei-an, LI Xiao-chuan. Symplectic Duality System on the Plane Magnetoelectroelastic Solids[J]. Applied Mathematics and Mechanics, 2006, 27(2): 177-185.
[7]	BIAN Wen-feng, WANG Biao, JIA Bao-xian. Mathematical Problems in the Integral-Transformation Method of Dynamic Crack[J]. Applied Mathematics and Mechanics, 2004, 25(3): 228-232.
[8]	ZHU Wei-ping, HUANG Qian. General Solution of the Overall Bending of Flexible Circular Ring Shells With Moderately Slender Ratio and Applications to the Bellows(Ⅳ)- Calculation for U-Shaped Bellows[J]. Applied Mathematics and Mechanics, 2002, 23(10): 1035-1040.
[9]	ZHU Wei-ping, HUANG Qian. General Solution of the Overall Bending of Flexible Circular Ring Shells With Moderately Slender Ratio and Applications to the Bellows(Ⅲ)- Calculation for C-Shaped Bellows[J]. Applied Mathematics and Mechanics, 2002, 23(10): 1025-1034.
[10]	ZHU Wei-ping, HUANG Qian. General Solution of the Overall Bending of Flexible Circular Ring Shells With Moderately Slender Ratio and Applications to the Bellows(Ⅱ)-Calculation for Omega-Shaped Bellows[J]. Applied Mathematics and Mechanics, 2002, 23(8): 798-804.
[11]	ZHU Wei-ping, HUANG Qian. General Solution of the Overall Bending of Flexible Circular Ring Shells With Moderately Slender Ratio and Applications to the Bellows(Ⅰ)-Governing Equation and General Solution[J]. Applied Mathematics and Mechanics, 2002, 23(8): 790-797.
[12]	Ding Haojiang, Guo Fenglin, Hou Pengfei. General Solutions of Coupled Thermoelastic Problem[J]. Applied Mathematics and Mechanics, 2000, 21(6): 573-577.
[13]	Zhang Xi-de, Du Tao, Zhang Wen, Shen Wen-jun. Correction for Housne’s Equation of Bending Vibration of a Pipe Line Containing Flowing Fluid[J]. Applied Mathematics and Mechanics, 1993, 14(2): 147-149.
[14]	Zhang Hong-qing, Yang Guang. Constructions of the General Solution for a System of Partial Differential Equations with Variable Coefficients[J]. Applied Mathematics and Mechanics, 1991, 12(2): 135-139.
[15]	Ji Zhen-yi. The General Solution for Axial Symmetrical Bending of Nonhomogeneous Circular Plates Resting on an Elastc Foundation[J]. Applied Mathematics and Mechanics, 1991, 12(9): 813-820.
[16]	Zheng Xiao-ping, Wang Shang-wen, Chen Bai-ping. General Solution for Dynamical Problem of Infinite Beam on an Elastic Foundation[J]. Applied Mathematics and Mechanics, 1991, 12(7): 593-597.
[17]	Zhao Xing-hua. The Improvement of the General Expression for the Stress Function φ of the Two-Dimensional Problem[J]. Applied Mathematics and Mechanics, 1990, 11(3): 195-202.
[18]	Huang He-ning, Wang Fa-jun. High-Order Boundary Conditions for the Problems of Laplace Equation in Infinite Region and Their Application[J]. Applied Mathematics and Mechanics, 1990, 11(11): 1013-1018.
[19]	Zhou Qing, Wang Min-zhong. A Discussion on “Representing General Solution of Equations in Theory of Elasticity by Harmonic Functions”[J]. Applied Mathematics and Mechanics, 1987, 8(11): 1035-1038.
[20]	Nie Yi-yong. Representing General Solution of Equations in Theory of Elasticity by Harmonic Functions[J]. Applied Mathematics and Mechanics, 1986, 7(2): 155-160.