Dynamic Analysis of Magnetoelasticity for Ferromagnetic Plates with Nonlinear Magnetization in Magnetic Fields
Publication: Journal of Engineering Mechanics
Volume 139, Issue 5
Abstract
Based on a generalized variational principle of magnetoelasticity and Hamilton’s principle, a dynamic theoretical model is developed for magnetoelastic vibration of a soft ferromagnetic plate with nonlinear magnetization being in a stationary magnetic field. The fundamental equations of the magnetic field and the motion of the ferromagnetic plate are derived together with the expression of equivalent magnetic force acting on the ferromagnetic plate as a result of the reciprocity between the magnetizable ferromagnetic plate and the applied field. There involve twofold nonlinearities in which one is from the magnetoelastic coupling and the other arises from the nonlinear magnetization of the ferromagnetic medium. A numerical technique that combines the finite-element method for magnetic-field distribution with the finite-difference and Newmark methods for vibration of the ferromagnetic plate is proposed. Analyses of the dynamic behaviors and stability characteristics of a ferromagnetic cantilevered beam-plate vibrating in an applied stationary magnetic field are implemented numerically, which show that the frequency of magnetoelastic vibration of the ferromagnetic beam-plate increases with the intensity and the incident angle of the applied magnetic field, and that the magnetization nonlinearity obviously influences the magnetoelastic dynamics behavior. Especially for strong magnetic fields and certain geometrical parameters of the ferromagnetic plate, the magnetoelastic dynamic behavior of the ferromagnetic plate, taking into account nonlinear magnetization, exhibits distinctive magnetoelastic characteristics compared with that of the ferromagnetic plate with linear magnetization.
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Acknowledgments
The authors acknowledge support by the National Natural Science Foundation of China (10872081 and 11172117), and the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (11121202).
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Published In
Journal of Engineering Mechanics
Volume 139 • Issue 5 • May 2013
Pages: 559 - 567
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Dec 8, 2009
Accepted: Aug 2, 2012
Published online: Aug 13, 2012
Published in print: May 1, 2013
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