Affiliations: [a] College of Science, China Agricultural University,
P.O. Box 74, Beijing 100083, P.R. China | [b] Institute of Mechanics, Department of Mechanical
Engineering, University of Kassel, Moenchebergstrasse 7, D-34125 Kassel, Germany
Abstract: Without employing ad hoc assumptions, various equations and
solutions for magnetoelastic beams are deduced systematically and directly from
the two-dimensional magnetoelasticity. These equations and solutions can be
used to construct the refined theory of magnetoelastic beams for tension and
compression deformation. By using the general solution for the soft
ferromagnetic elastic solids and the Lur'e method, the refined theory can now
be explicitly established. In the case of homogeneous boundary conditions, the
exact governing differential equations and solutions for beams are derived,
which consist of three governing differential equations. In the case of
non-homogeneous boundary conditions, a traction free boundary condition is
considered. In two illustrative examples of beams, it is shown that the exact
or accurate solutions can be obtained in use of the refined theory deduced herein.
Keywords: Magnetoelastic beams, tension and compression deformation, the refined theory, governing equation
