Several Problems Of Magntoelectroelasticity

Based on the basic relations of mechanics, electrics and magnetics, the governing equations which are expressed in term of displacements of ux,uy and uz, electric potential Ω and magnetic potential ψ are derived for transversely isotropic magnetoelectroelastic medium. By introducing two displacements functions ψ and G, two groups variables which department ψ and G from u,, Ω and ψ can be expressed as formerly as differential equations D F = 0. Solving the equation, the general solutions of the governing equations and corresponding general displacements and stresses of equilibrium case are obtained in terms of ψ and F .The Green's function of infinite and half-infinite space, the solutions of a cone under concentrated loads at its apex, and rotating circular and annular plate of magnetoelectroelastic medium are obtained by use of these solutions and given boundary conditions. From these dynamic solutions, frequency and mode shapes of sectorial plate and sectorial annular plate under boundary conditions of GSS and GRS are derived. The three-dimensional exact solutions of the displacement, electric potential, magnetic potential, stress, electric displacement and magnetic induction of equilibrium problems are also obtained. These solutions can be degenerated to corresponding ones of circular and annular plate in cases of axisymmetry and non-axisymmetry.The frequency and mode shapes of the multilayered axisymmetric circular and annular plate with boundary conditions of GSS and GRS are derived by utilizing the state space method. The 3-D exact solutions of corresponding static problems are also given.