Summary.
The problem of deducing a one-dimensional theory from a three-dimensional theory for a soft ferromagnetic elastic isotropic body is investigated. Based on the linear magnetoelasticity, the refined theory of magnetoelastic beams is presented by using the general solution for the soft ferromagnetic elastic solids and the Lur’e method. Based on the refined theory of magnetoelastic beams, the exact equations and solutions for the homogeneous beams are derived and the equations can be decomposed into three governing differential equations: the fourth-order equation, the transcendental equation and the magnetic equation. Moreover, the approximate equations and solutions for the beam under transverse loadings and magnetic field perturbations are derived directly from the refined beam theory. By omitting higher order terms and coupling effects, the refined beam theory can be degenerated into other well-known elastic and magnetoelastic theoretical models.
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Acknowledgments.
Support from the National Natural Science Foundation of China (Project No. 10172003 and 10372003) is acknowledged.
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Gao, Y., Wang, M. The refined theory of magnetoelastic rectangular beams. Acta Mechanica 173, 147–161 (2004). https://doi.org/10.1007/s00707-004-0171-5
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DOI: https://doi.org/10.1007/s00707-004-0171-5