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Analytical solutions for density functionally gradient magneto-electro-elastic cantilever beams
Haojiang Ding,Aimin Jiang 국제구조공학회 2007 Smart Structures and Systems, An International Jou Vol.3 No.2
The general solution for two-dimensional magneto-electro-elastic media in terms of four harmonic displacement functions is proposed analytically. The expressions of specific solutions of magneto-electro-elastic plane problems with specific body forces are derived. Finally, based on the general solution in the case of distinct eigenvalues and the specific solution for density functionally gradient media, two kinds of beam problems with body forces depending only on the z or x coordinate are solved by the trial-and-error method.
Analytical solutions for density functionally gradient magneto-electro-elastic cantilever beams
Jian, Aimin,Ding, Haojiang Techno-Press 2007 Smart Structures and Systems, An International Jou Vol.3 No.2
The general solution for two-dimensional magneto-electro-elastic media in terms of four harmonic displacement functions is proposed analytically. The expressions of specific solutions of magneto-electro-elastic plane problems with specific body forces are derived. Finally, based on the general solution in the case of distinct eigenvalues and the specific solution for density functionally gradient media, two kinds of beam problems with body forces depending only on the z or x coordinate are solved by the trial-and-error method.
Analytical solutions to magneto-electro-elastic beams
Jiang, Aimin,Ding, Haojiang Techno-Press 2004 Structural Engineering and Mechanics, An Int'l Jou Vol.18 No.2
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.
Chen, Jiangying,Xu, Rongqiao,Huang, Xusheng,Ding, Haojiang Techno-Press 2006 Structural Engineering and Mechanics, An Int'l Jou Vol.23 No.2
The axisymmetric free vibrations of transversely isotropic magnetoelectroelastic laminated circular plates are studied. Based on the three-dimensional governing equations of magnetoelectroelastic medium, the state space equations of laminated circular plates are obtained. By using the finite Hankel transform and rendering the free terms left by the transform in terms of the boundary quantities, the solutions of the state space equations are given for two kinds of boundary conditions. The frequency equations of the free vibration are derived using the propagator matrix method and the boundary conditions at top and bottom surfaces. By virtue of the inverse Hankel transform, the mode shapes are also determined. Since the solutions strictly satisfy the governing equations in the region and the boundary conditions at the edges, they are the three-dimensionally exact. Finally, the natural frequencies of such plates are tabulated and compared with those of the piezoelectric and elastic plates in the numerical example.