摘要
对处于横向均匀磁场中四边简支的软铁磁矩形薄板,在横向均布载荷作用下,主要考虑因磁化和涡电流引起的磁场力作用,由伽辽金法推导出磁弹性振动微分方程,求得了系统的同宿轨道参数方程;并推导和求解了振动系统的同宿轨道的Melnikov函数,给出了判断该系统发生Smale马蹄变换意义下混沌振动的条件和混沌判据,进一步应用Matlab程序对系统的混沌特性进行了数值模拟,得到相应的相图、庞加莱截面图和时程曲线图,验证了混沌现象的存在。
For a soft ferromagnetic rectangular thin plate with four edges simply supported under transverse uniform magnetic field and transverse uniform load, the vibration differential equation is derived with Garierkin method mainly considering magnetization and eddy current. Furthermore, the homoclinic orbit parameter equations of this thin plate vibration system are acquired. Using Melnikov function method, the homoclinic orbit’s Melnikov function of the vibration system are derived and solved. Finally, the chaos condition and the judging criterion for this system about Smale commutation are given. Matlab soft ware is applied to simulate the chaotic characteristic of the system. The phase diagram, Poincare section diagram and the time-history curves of the displacement show the existence of chaos.
出处
《振动与冲击》
EI
CSCD
北大核心
2008年第9期87-89,99,共4页
Journal of Vibration and Shock
基金
国家自然科学基金项目(10372067)
国家自然科学基金项目(10772129)
山西省青年基金资助项目(20060211007)
关键词
软铁磁矩形薄板
磁弹性
同宿轨道
混沌运动
MELNIKOV函数
数值模拟
soft ferromagnetic rectangular thin plate
magnetoelastic
homoclinic orbit
chaotic vibration
Melnikov function
numerical simulation
