| Based on the mechanical, electric and magnetic equations of transversely isotropic magneto-electro-elastic medium, this paper studys the effects on magneto-electro-elastic coupling of magneto-electric(ME) materials by various factors, such as, material parameters, boundary conditions, external applied loadings, and gradient effects, et.For the multi-layered magneto-electro-elastic cantilever beam, firstly, the force model when ME beam are subjected to the complicated loadings is established. Then, based on the constitutive equation, geometric equation and boundary condition, the corresponding expressions of displacement and rotation angle for ME beam, which under various boundary conditions and complicated loadings, are derived. It proves that the material parameters, delamination ratio and layer number of ME beam, thickness of elastic layer embedded into ME beam and applied loadings have great effects on the ME response characteristics of magneto-electro-elastic cantilever beam.For the functionally graded ME beam, based on the constitutive equation of two dimensional magneto-electro-elastic medium in two dimensional plane, several basic solutions on magneto-electro-elastic coupling problems for functionally graded ME beam, considering the grade effects, are derived by semi-inverse method. It proves that the electric and magnetic parameters of ME materials have nothing to do with stress componentsσz andτxz, while have effects on stress componentσx and all the strain and displacement components. The solutions to the cantilever beam with constant volume force and without volume force can be derived from the one to functionally graded cantilever beam.The analytical solutions obtained in this paper are not only helpful for the further study on the ME response characteristics of ME materials subjected to more complicated loadings and boundary conditions, but supplys theoretical basis for the structure and performance optimization design of ME devices. |
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