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http://dx.doi.org/10.12989/sem.2004.18.2.195

Analytical solutions to magneto-electro-elastic beams  

Jiang, Aimin (West Branch of Zhejiang University of Technology)
Ding, Haojiang (Department of Civil Engineering, Zhejiang University)
Publication Information
Structural Engineering and Mechanics / v.18, no.2, 2004 , pp. 195-209 More about this Journal
Abstract
By means of the two-dimensional basic equations of transversely isotropic magneto-electro-elastic media and the strict differential operator theorem, the general solution in the case of distinct eigenvalues is derived, in which all mechanical, electric and magnetic quantities are expressed in four harmonic displacement functions. Based on this general solution in the case of distinct eigenvalues, a series of problems is solved by the trial-and-error method, including magneto-electro-elastic rectangular beam under uniform tension, electric displacement and magnetic induction, pure shearing and pure bending, cantilever beam with point force, point charge or point current at free end, and cantilever beam subjected to uniformly distributed loads. Analytical solutions to various problems are obtained.
Keywords
general solution; magneto-electro-elastic plane; harmonic function; analytical solution;
Citations & Related Records

Times Cited By Web Of Science : 16  (Related Records In Web of Science)
Times Cited By SCOPUS : 22
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1 Ding, H.J., Wang, G.Q. and Chen, W.Q. (1997a), "General solution of plane problem of piezoelectric media expressed by "harmonic functions"", Applied Mathematics and Mechanics, 18, 757-764.   DOI   ScienceOn
2 Ding, H.J., Wang, G.Q. and Chen, W.Q. (1997b), "Green's functions for a two-phase infinite piezoelectric plane", Proc. of Royal Society of London(A), 453, 2241-2257.   DOI   ScienceOn
3 Pan, E. (2001), "Exact solution for simply supported and multilayered magneto-electro-elastic plates", J. Appl. Mech., ASME, 68, 608-618.   DOI   ScienceOn
4 Sosa, H.A. and Castro, M.A. (1994), "On concentrated loads at the boundary of a piezoelectric half-plane", J. Mech. Phys. Solids, 42(7), 1105-1122.   DOI   ScienceOn
5 Wang, X. and Shen, Y.P. (2003), "Inclusion of arbitrary shape in magneto-electro-elastic composite materials", Int. J. Eng. Sci., 41, 85-102.   DOI   ScienceOn
6 Pan, E. (2002a), "Three-dimensional Green's function in anisotropic magneto-electro-elastic bimaterials", Z. Angew. Math. Phys., 53, 815-838.   DOI   ScienceOn
7 Timoshenko, S.P. and Goodier, T.N. (1970), Theory of Elasticity, 3rd McGraw-Hill Book Co., N.Y.
8 Wang, X. and Shen, Y.P. (2002), "The general solution of three-dimensional problems in magneto-electro-elastic media", Int. J. Eng. Sci., 40, 1069-1080.   DOI   ScienceOn
9 Chen, J.Y., Ding, H.J. and Hou, P.F. (2003), "Analytical solutions of simply supported magneto-electro-elastic circular plate under uniform loads", J. of Zhejiang University SCIENCE, 4(5), 560-564.   DOI
10 Hou, P.F., Leung, Andrew Y.T. and Ding, H.J. (2003), "The elliptical Hertizan contact of transversely isotropic magneto-electro-elastic bodies", Int. J. Solids Struct., 40, 2833-2850.   DOI   ScienceOn
11 Pan, E. (2002b), "Free vibrations of simply supported and multilayered magneto-electro-elastic plates", J. of Sound Vib., 252(3), 429-442.   DOI   ScienceOn
12 Kogan, L., Hui, C.Y. and Molkov, V. (1996), "Stress and induction field of a spheroidal inclusion or a pennyshaped crack in a transversely isotropic piezoelectric material", Int. J. Solids Struct., 33(19), 2719-2737.   DOI   ScienceOn
13 Liu, J.X., Liu, X.L. and Zhao, Y.B. (2001), "Green's functions for anisotropic magneto-electro-elastic solids with an elliptical cavity or a crack", Int. J. Eng. Sci., 39, 1405-1418.   DOI   ScienceOn