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Magnetoelastic ultraharmoniccombination resonance of a rotating circle plate in magnetic field |
HU Yuda1,2 ,QIN Xiaobei1,2 |
1. School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao 066004, China;
2. Key Laboratory of Mechanical Reliability for Heavy Equipment and Large Structures of Hebei Province, Yanshan University, Qinhuangdao 066004, China |
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Abstract Aiming at a rotating conductive circle plate in magnetic field, based on the theory of elastic and electromagnetic principle, the kinetic energy, strain energy and electromagnetic forced expressions of rotating plate were obtained. Applied the Hamilton theory, the electroelastic transverse vibration equation of circular plate under the condition of geometric nonlinear was set up. The axisymmetric problem of a circular plate under the dualfrequency excitations in a transverse magnetic field was analyzed, and the nondimensional differential equation of vibration of the rotating plate was obtained by the Galerkin integral method. The multiscale method was used to solve the nonlinear equation, and the amplitude frequency response equation of the system with ultraharmoniccombination resonance was received, and the stability of steady solution was analyzed. An example was given to show the curves of the resonance amplitude of the rotating circular plate with frequency parameters, magnetic field and force amplitude, and the effects of rotational speed and magnetic field on the steadystate solution were analyzed; by analyzing the trend of the phase trajectory near the singularity on the plot of the moving phase, the multivalue and stability of the steady state solution were further elucidated.
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Received: 18 January 2017
Published: 15 June 2018
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