国家自然科学基金重点项目(10732020)、国家自然科学基金项目(11072008)
利用高维非线性系统的Hopf分叉定理,研究复合材料层合板的双Hopf分叉.研究了一类受面内激励和横向外激励联合作用下的复合材料层合板在主参数共振—1∶1内共振情况下的双Hopf分叉.首先利用多尺度法得到系统的平均方程,经过简化得到了系统的分叉响应方程.根据对分叉响应方程的分析,得到了系统平衡解的稳定性临界曲线,并给出了系统产生双Hopf分叉的条件.利用数值方法得到系统在参数平面上的分叉集,通过对不同分叉区域的分析,我们发现随着参数的变化复合材料层合板存在不同的周期运动现象.
A?composite?laminated?thin?plate?was?studied?for?analyzing?the?dynamic?behavior?near?a?critical?point?characterized?by?initial?resonance.?Based?on?the?averaged?equations,?the?transition?boundaries?were?sought?to?divide?the?parameter?space?into?a?set?of?regions,?which?correspond?to?different?types?of?solutions.?The?Hopf?bifurcation?theorem?was?used?to?investigate?the?stable?conditions?of?respective?equilibrium?points.?Then,?the?conditions?of?the?occurrence?of?double?Hopf?bifurcations?were?found,?and?two?types?of?periodic?solutions?may?bifurcate?from?the?initial?equilibrium.?Based?on?bifurcation?theory,?it?is?shown?that?the?composite?laminated?thin?plates?exhibit?different?periodic?motions.
周艳,张伟.复合材料层合板的双Hopf分叉分析[J].动力学与控制学报,2015,13(3):161~164; Zhou Yan, Zhang Wei. Doublehopf bifurcations of composite laminated thin plate[J]. Journal of Dynamics and Control,2015,13(3):161-164.
