HU Yu-da, ZHANG Li-bao. Magneto-Elastic Vibration Equations for Axially Moving Conductive and Magnetic Beams[J]. Applied Mathematics and Mechanics, 2015, 36(1): 70-77. doi: 10.3879/j.issn.1000-0887.2015.01.006
 Citation: HU Yu-da, ZHANG Li-bao. Magneto-Elastic Vibration Equations for Axially Moving Conductive and Magnetic Beams[J]. Applied Mathematics and Mechanics, 2015, 36(1): 70-77.

# Magneto-Elastic Vibration Equations for Axially Moving Conductive and Magnetic Beams

##### doi: 10.3879/j.issn.1000-0887.2015.01.006
Funds:  The National Natural Science Foundation of China(11472239)
• Rev Recd Date: 2014-10-06
• Publish Date: 2015-01-15
• The magneto-elastic coupled vibration theoretical model for axially moving conductive and magnetic beams in magnetic field environment was studied. Based on the Timoshenko beam theory and with the geometric nonlinearity considered, the expressions for the deformation potential energy, kinetic energy, electromagnetic force and the virtual work of mechanical force of the elastic beam in axial motion and lateral bidirectional vibration were gained. Then the Hamilton variational principle was applied to get the nonlinear magneto-elastic coupled vibration equations for the axially moving Timoshenko beam in a magnetic field, and get those for the simplified Euler-Bernoulli beam. Based on the electromagnetic theory and the constitutive relation of the corresponding electromagnetism, the expressions for the electromagnetic force of the current-conducting elastic beam, and for the magnet force and magnet force couple of the magneto-elastic beam based on the magnetic dipole-current loop model, were derived. Through the numerical example, the singularity distribution and stability of the conductive and elastic beam in axial movement were analyzed.
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