Refined analysis of axi-symmetric circular cylinder in the axial magnetic field without ad hoc assumption

The refined theory for axi-symmetric magnetoelastic circular cylinder is deduced systematically and directly from linear magnetoelasticity theory. Based on the general solution of magnetoelastic equation and the Lur’e method, the refined theory yields the solutions for magnetoelastic circular cylinder without ad hoc assumptions. On the basis of the refined theory developed in the present study, solutions are obtained for magnetoelastic circular cylinder with homogeneous and non-homogenous boundary conditions, respectively. For the circular cylinder with homogeneous boundary conditions, the refined theory provides exact solutions that satisfy all of the governing equations. The exact solutions can be divided into three parts: the 2-orders equation, the transcendental equation, and the magnetic equation. In the case of non-homogenous boundary conditions, the approximate governing equations are accurate up to the high-order terms with respect to cylinder radius.