研究旋转运动圆形薄板在磁场中受到机械载荷作用时的磁弹性非线性共振问题。根据哈密顿原理推导出旋转运动圆板在磁场中的磁弹性非线性振动方程，基于电磁理论给出了旋转板所受电磁力的表达式。通过位移函数的设定并应用伽辽金积分法，得到横向磁场中旋转导电圆板的磁弹性轴对称振动微分方程。应用平均法对系统非线性主共振问题进行求解，得到稳态运动下的幅频响应方程。通过数值计算，得到固支边界条件下圆板的幅频特性曲线以及振幅随磁感应强度、转速、激励力等参数的变化规律曲线图，分析了不同参数对旋转板共振幅值及非线性特性的影响。
Abstract
The nonlinear resonance of a conductive rotating thin circular plate subjected to mechanical loads in magnetic field was investigated. The nonlinear vibration equation about the spinning round plate was derived according to Hamilton principle. Based on the electromagnetic theory, the expressions of electromagnetic forces were derived. According to the set of a displacement function, the magnetoelastic forced vibration differential equation of the round plate was obtained through the application of Galerkin integral method. By mean of averaging method, the amplitude-frequency response equation in steady state was established. The amplitude frequency characteristic curves and the relationship curves of amplitude changing with the magnetic induction intensity, the speed of rotation and the excitation force of the plate with fixed boundary condition were obtained according to the numerical calculation. The influence of different parameters on the amplitude and the nonlinear characteristics of the spinning plate was analyzed finally.
关键词
导电圆板 /
旋转运动 /
主共振 /
磁场 /
平均法
{{custom_keyword}} /
Key words
conductive round plate /
rotary motion /
primary resonance /
magnetic filed /
averaging method
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1]. Yalcin H S, Arikoglu A, Ozkol I. Free vibration analysis of circular plates by differential transformation method [J]. Applied Mathematics and Computation, 2009, 212(2): 377~386
[2]. Zhou D, Au F T K, Cheung Y K, et al. Three-dimensional vibration analysis of circular and annular plates via the Chebyshev–Ritz method [J]. International Journal of Solids and Structures, 2003, 40(12): 3089~3105
[3]. Jeong K H. Free vibration of two identical circular plates coupled with bounded fluid [J]. Journal of Sound and Vibration, 2003, 260(4): 653~670
[4]. Gao Yuanwen, Xu Bang, Huh H. Electromagneto-thermo-mechanical behaviors of conductive circular plate subject to time-dependent magnetic fields [J]. Acta Mechanics, 2010, 210(1-2): 99~116.
[5]. Hu Yuda, Li Jing. Magneto-elastic combination resonances analysis of current-conducting thin plate [J]. Applied Mathematic and Mechanics (English Edition), 2008, 29(8): 1053~1066.
[6]. Hu Yuda, Li Jing. The magneto-elastic subharmonic resonances of current-conducting thin plate in magnetic field [J]. Journal of Sound and Vibration, 2009, 319(3-5): 1107~1120.
[7]. 胡宇达, 张金志. 轴向运动载流导电板磁热弹性耦合动力学方程[J]. 力学学报, 2013, 45(5): 792~796 (Hu Yuda, Zhang Jinzhi. Magneto-thermo-elastic coupled dynamic equations of axially moving carry current plate in magnetic field [J]. Acta Mechanica Sinica, 2013, 45(5): 792~796 (in Chinese) )
[8]. 胡宇达, 杜国君. 磁场环境下导电圆形薄板的磁弹性强迫振动[J]. 工程力学, 2007, 24(7): 184~187 (Hu Yuda, Du Guojun. Forced vibration of a thin round conductive plate in magnetic field [J]. Engineering Mechanics, 2007, 24(7): 184~187 (in Chinese) )
[9]. Hashemi S H, Farhadi S, Carra S. Free vibration analysis of rotating thick plates [J]. Journal of Sound and Vibration, 2009, 323(1-2): 366~384
[10]. Maretic R. Transverse vibration and stability of an eccentric rotating circular plate [J]. Journal of Sound and Vibration, 2005, 280(3-5): 467~478
[11]. Bauer H F, Eidel W. Transverse vibration and stability of spinning circular plates of constant thickness and different boundary conditions [J]. Journal of Sound and Vibration, 2007, 300(3-5): 877~895
[12]. Allahverdizadeh A, Naei M H, Nikkhah B M. Nonlinear free and forced vibration analysis of thin circular functionally graded plates [J]. Journal of Sound and Vibration, 2008, 310(4-5): 966~984
[13]. Chen Yuren, Chen Lienwen. Vibration and stability of rotating polar orthotropic sandwich annular plates with a viscoelastic core layer [J]. Composite Structures, 2007, 78(1): 45~57
[14]. 李龙飞, 王省哲, 周又和. 粘弹性夹芯层合旋转圆板的气动弹性动力稳定性分析[J]. 固体力学学报, 2013, 34(4): 325~332 (Li Longfei, Wang Xingzhe, Zhou Youhe. Analysis on aeroelastic dynamic stability of a rotating sandwich annular plate with viscoelastic core layer [J]. Acta Mechanic Solida Sinica, 2013, 34(4): 325~332 (in Chinese) )
[15]. 赵飞云, 洪嘉振, 刘锦阳, 等. 高速旋转柔性矩形薄板的动力学建模和近似算法[J]. 振动工程学报, 2006, 19(3): 416~421 (Zhao Feiyun, Hong Jiazhen, Liu Jinyang, et al. Dynamic modeling and modal truncation approach for a high-speed rotating thin elastic rectangular plate. Journal of Vibration Engineering [J], 2006, 19(3): 416~421 (in Chinese) )
[16]. 徐芝纶. 弹性力学[M]. 北京: 高等教育出版社, 2006 (Xu Zhilun. Elasticity[M]. Beijing: Higher Education Press, 2006 (in Chinese)
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}
PDF(1514 KB)
