横向磁场中矩形薄板在分布载荷作用下混沌分析

在建立置于横向稳恒电磁场中,同时受横向均布载荷作用四边简支的金属矩形薄板的受力模型的基础上,推导了金属矩型薄板的磁弹性耦合动力学方程,求得了该模型振动系统的异宿轨道参数方程,并根据Melnikov函数方法,推导并求解了振动系统的异宿轨道的Melnikov函数,最后给出了判断该系统发生Smale马蹄变换意义下混沌运动的条件和混沌运动判据.由此可对矩形薄板在机械载荷和电磁载荷共同作用下的分岔和混沌进行分析.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问题的研究.

THE CHAOS ANALYSIS OF RECTANGULAR PLATE UNDER DISTRIBUTED LOAD IN TRANSVERSE MAGNETIC FIELD(I)

In this paper, the model for thin rectangular plate coupled transverse invariable electro-magnetic with uniform transverse forces was built.The boundary of this model was that four edges were simply supported. Based on this, the coupled vibration equations of thin rectangular plate were derived, and the heteroclinic orbit parameter equations of this thin plate vibration system were solved. Using Melnikov function method, the heteroclinic orbit's Melnikov function of vibration system were derived and solved. Finally, the chaos condition and judging criterion of this system about Smale commutation were given.Thus, we can study the bifurcation and chaos of thin rectangular plate coupled mechanical loads with electro-magnetic. The method offered in this paper may be used to study the elastic-magnetic vibration of thin plate under different boundary conditions and different external loads.