横向磁场中矩形薄板在分布载荷作用下混沌分析
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国家自然科学基金资助项目(50275128)


The chaos analysis of rectangular plate under distributed load in transverse magnetic field(Ⅱ)
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    摘要:

    在应用Melnikov函数方法,给出受横向分布载荷作用下,矩形薄板的磁弹性耦合系统发生混沌运动的条件和混沌运动判据的基础上,建立了Duffing振动系统的微分方程,针对薄板的磁弹性耦合振动系统做了混沌运动分析.应用Matlab程序,对系统的混沌特性作了仿真实验分析,给出了不同γ值时的相图和位移波形图,并将本文(Ⅰ)中Melnikov函数法的判断条件与仿真结果作比较,两者的结果是一致的,而且仿真实验反映的混沌更具有丰富的数字特性.本文给出的方法可以推广到其他不同边界条件和不同外载荷条件下弹性薄板的磁弹性振动

    Abstract:

    Under the conditions of chaos and on the basis of the chaos criterion for the system about Smale horse hoof commutation of thin rectangular plate in the transverse electromagnetic field under distributed transverse loads, the differential equations of Duffing vibration system were built by the method of Melnikov function. The chaotic motion of the coupled vibration of the thin elasticmagnetic plate was analyzed.The vibration system was simulated by Matlab program, the chaotic characteristics were analyzed, and the phase diagrams and wave diagrams of displacement with different γwere obtained.The results were compared with those obtained by Melnikov function method in paper (Ⅰ), and the two results were identical. The chaotic motion of the simulating experiment was of more digital characteristics. The method in this paper can be extended to study the elasticmagnetic vibration of thin plate under different boundary conditions and different external loads.

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朱为国,白象忠.横向磁场中矩形薄板在分布载荷作用下混沌分析[J].动力学与控制学报,2006,4(3):234~241; Zhu Weiguo, Bai Xiangzhong. The chaos analysis of rectangular plate under distributed load in transverse magnetic field(Ⅱ)[J]. Journal of Dynamics and Control,2006,4(3):234-241.

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  • 收稿日期:2005-11-26
  • 最后修改日期:2006-02-14
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