双铰四次弹性拱的混沌行为研究

Chaotic behavior of forth-order elastic arch with two hinge supports

对双铰四次弹性拱的混沌行为在横向周期荷载下的混沌行为进行了研究。首先利用拱的单元平衡方程建立了拱的二阶三次非线性动力学模型;然后通过变换使方程转化为不含常数项的非线性微分动力系统,并由此得到无扰动系统的3个不动点(一个鞍点,两个中心)与同宿轨道;再用Melnikov函数法给出了发生混沌的临界条件;最后给出了该系统出现定常运动和混沌运动的数值结果。研究表明四次弹性拱在横向周期荷载作用下的外激励振幅在一定范围内会出现混沌现象。

The chaotic behavior of the forth-order elastic arch with two hinge supports subjected to a transverse distributed varying periodic excitation is studied. Based on the equilibrium equation of an arch element the cubic nonlinear dynamic model with second order is established and the nonlinear differential dynamic system without constant term is obtained through a transfer process of T = U ＋ b. Hence three fixed points （one saddle point, two centers） and the homoclinic orbits are found. The critical condition of the chaotic vibration of the elastic arch is given by using the method of Melnikov function. The numerical results of the stationary and chaotic motion are given and discussed. The motion of forth-order elastic arch with two hinge supports subjected to a transverse periodic excitation may be chaotic motion when the amplitude is in the certain region.