轴向流作用下板状叠层结构的Hopf分叉

Hopf Bifurcation of Parallel Plate-type Structure in Axial flow

研究轴向流作用下板状叠层结构在三次非线性弹簧约束下的Hopf分叉。假设各板在同一时刻有相同的变形 ,建立轴向流作用下悬臂板状梁的三次非线性模型 ,采用Galerkin方法将偏微分方程化为常微分方程 ,并利用Hopf分叉代数判据得到系统临界流速及相应线性系统纯虚根的解析表达式 ,最后用数值方法模拟了理论结果。

The Hopf bifurcation of plate-type beams with cubic nonlinear stiffness in axial flow was studied. By assuming that all the plates have the same deflections at any instant, the nonlinear model of cantilevered plate-type beam in axial flow was established. The partial diferential equation was turned into an ordinary differential equation by using Galerkin method. A new algebraic criterion of Hopf bifurcation was utilized to get the analytic expression of critical flow velocity of the nonlinear system and the purely imaginary eigenvalues of the corresponding linear system. At last, the Forth order Runge-Kutta numerical method was applied to certify the theories.