Principal resonance characteristics and static load effect of a ferromagnetic circular plate in a transverse constant magnetic field

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Journal of Vibration and Shock ›› 2021, Vol. 40 ›› Issue (1) : 308-316.

MA Bingbing 1,2 HU Yuda 1,2

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Abstract

The principal resonance of a ferromagnetic circular plate in transverse constant magnetic field was studied. Based on the theory of electromagnetism, the magnet force and Lorentz force acting on a circular plate in a constant magnetic field were obtained.Applying Hamiltonian variational principle, the differential equation of magnetoelastic transverse vibration of ferromagnetic circular plate in magnetic field was derived.The magnet force acting on a ferromagnetic circular plate in a constant magnetic field is a static load. The initial deflection of a ferromagnetic circular plate under static load and clamped boundary was obtained by Galerkin method. The first and second order approximate solutions of the nonlinear equations under periodic loads were obtained by multiscale method, and the amplitude-frequency response equations of the principal resonance were obtained. Through numerical examples, the amplitude-frequency curves, the curves of amplitude varying with magnetic field intensity and excitation force were obtained. The effects of plate thickness, magnetic field intensity and excitation force on resonance amplitude were analyzed, and the differences between two approximations were compared.The results show that the amplitude increases significantly in the resonance region, and the first-order approximation is similar to the second-order approximation when the magnetic field intensity is low, while the second-order approximation is more accurate when the magnetic field intensity is high.

Key words

ferromagnetic circular plate / constant magnetic field / magnetoelasticity / principal resonance / multiscale method

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MA Bingbing 1,2 HU Yuda 1,2. Principal resonance characteristics and static load effect of a ferromagnetic circular plate in a transverse constant magnetic field[J]. Journal of Vibration and Shock, 2021, 40(1): 308-316

References

[1] OKAJIMA M, BURROUGHS C B, CHARPIE J P. An analytic model for the frequencies of resonance of rectangular plates of variable curvature and thickness[J]. The Journal of the Acoustical Society of America, 1995, 97(2): 1053-1060.
[2] OH K, NAYFEH A H. Nonlinear combination resonances in cantilever composite plates[J]. Nonlinear Dynamics, 1996, 11(2): 143-169.
[3] DU G J, LIU X M, HU Y D, et al. Nonlinear superharmonic resonance of damped circular sandwich plates with initial deflection[J]. Advanced Materials Research, 2011, 199-200: 1080-1083.
[4] 高原文, 周又和, 郑晓静. 横向磁场激励下铁磁梁式板的混沌运动分析[J]. 力学学报, 2002, 34(1): 101-108.
GAO Yuan-wen, ZHOU You-he, ZHENG Xiao-jing. Analysis of chaotic motion of geometrically nonlinear ferromagnetic beam-plates excited by transverse magnetic fields[J]. Acta Mechanica Sinica, 2002, 34(1): 101-108.
[5] XUE C X, REN X J. Nonlinear principal resonance of magneto-electro-elastic thin plate[J]. Journal of Measurement Science & Instrumentation, 2014, 5(4): 93-98.
[6] 张小广, 胡宇达, 任兴利. 四边固支功能梯度矩形板的主共振分析[J]. 振动与冲击, 2011, 30(6):153-157.
ZHANG Xiao-guang, HU Yu-da, REN Xing-li. Nonlinear principle resonance of clamped functionally graded rectangular plate[J]. Journal of Vibration and Shock, 2011, 30(6): 153-157.
[7] HU Y D, LI J. The magneto-elastic subharmonic resonance of current-conducting thin plate in magnetic field[J]. Journal of Sound & Vibration, 2009, 319(3): 1107-1120.
[8] 胡宇达, 秦晓北. 磁场中旋转运动圆板磁弹性超谐-组合共振[J]. 振动与冲击, 2018, 37(12): 167-173+192.
HU Yu-da, QIN Xiao-bei. Electro-magnetic elastic harmonic resonance analysis of a periphery fixed rotating circular plate[J]. Journal of Sound & Vibration, 2018, 37(12): 167-173+192.
[9] HU Y D, LI W Q. Study on primary resonance and bifurcation of a conductive circular plate rotating in air-magnetic fields[J]. Nonlinear Dynamics, 2018, 93(2): 671-687.
[10] CHEN J, ZHANG W, SUN M, et al. Parametric study on nonlinear vibration of composite truss core sandwich plate with internal resonance[J]. Journal of Mechanical Science & Technology, 2016, 30(9): 4133-4142.
[11] YAMAKI N, OTOMO K, CHIBA M. Non-linear vibrations of a clamped circular plate with initial deflection and initial edge displacement, part I: Theory[J]. Journal of Sound &Vibration, 1981, 79(1): 23-42.
[12] WANG J Y，CHEN K J. Vibration problems of flexible circular plates with initial deflection[J]. Applied Mathematics & Mechanics, 1993, 14(2): 177-184.
[13] DU G J, MA J Q. Nonlinear vibration and buckling of circular sandwich plate under complex load[J]. Applied Mathematics and Mechanics, 2007, 28(8): 1081-1091.
[14] 王永岗, 戴诗亮. 具有初挠度的受热双层金属圆板的混沌运动[J]. 清华大学学报(自然科学版), 2004, 44(8): 1134-1137.
WANG Yong-gang, DAI Shi-liang. Chaotic motion of a heated bimetallic thin circular plate with initial deflection[J]. Journal of Tsinghua University (Natural Science Edition), 2004, 44(8): 1134-1137.
[15] HU Y D, WANG T. Nonlinear free vibration of a rotating circular plate under the static load in magnetic field[J]. Nonlinear Dynamics, 2016, 85(3): 1825-1835.
[16] HU Y D, WANG T. Nonlinear resonance of the rotating circular plate under static loads in magnetic field[J]. Chinese Journal of Mechanical Engineering, 2015, 28(6): 1277-1284.
[17] 徐学平, 韩勤锴, 褚福磊. 静载荷作用下偏心转子电磁振动特性[J]. 清华大学学报(自然科学版), 2016, 56(2): 176-184.
XU Xue-ping, HAN Qin-kai, CHU Fu-lei. Electromagnetic vibration characteristics of an eccentric rotor with a static load[J]. Journal of Tsinghua University (Natural Science Edition), 2016, 56(2): 176-184.
[18] 王德禹. 预静载荷作用矩形板的冲击屈曲[J]. 上海交通大学学报, 1996, 30(5): 37-41.
WANG De-yu. The impact buckling of pre-statically loaded rectangular plate[J]. Journal of Shanghai Jiaotong University, 1996, 30(5): 37-41.
[19] BABICH S Y, GLUKHOV Y P. Bending a plate on prestressed elastic foundation under live static load[J]. International Applied Mechanics, 2017, 53(2): 1-13.
[20] 周又和, 郑晓静. 电磁固体力学[M]. 北京: 科学出版社, 1999.
ZHOU You-he, ZHENG Xiao-jing. Electromagnetic solid mechanics[M]. Beijing: Science Press, 1999.
[21] ZHOU Y H, MIYA K. A Theoretical prediction of natural frequency of a ferromagnetic beam plate with low susceptibility in an in-plane magnetic field[J]. Journal of Applied Mechanics, 1998, 65(1): 121-126.