运动约束亚音速二维粘弹性壁板的非线性颤振

Nonlinear Flutter of a Two-Dimensional Viscoelastic Plate with Motion Constraints in Subsonic Flow

为研究粘弹性悬臂壁板在亚音速气流和非线性运动约束联合作用下的稳定性及非线性颤振,基于Hamilton原理建立了悬臂壁板的运动方程,并采用Galerkin方法将其转化为常微分方程组,在参数平面内研究了系统的颤振失稳及发散失稳边界.采用数值模拟方法并根据不同的运动响应将颤振失稳区划分为3个子区域,研究了颤振失稳区内,系统复杂的运动响应.结果表明:系统出现了颤振失稳;非线性因素系统在颤振失稳后处于极限环运动状态;周期-3运动及周期-5运动会伴随着混沌运动产生;随着动压的增大,系统最后将呈现发散运动.

In order to study the stability and nonlinear flutter of a cantilevered viscoelastic plate with nonlinear motion constraints in subsonic flow, the motion equation of the cantilevered plate is established by Hamilton theory. The equation is then transformed to a series of ordinary differential equations using the Galerkin method;the flutter and divergence is addressed and their boundaries are presented in a two-parameter space. The complex nonlinear behavior in the region of flutter instability is investigated using numerical simulations. The flutter region is divided into three subregions according to different types of plate motions. Results show that the plate loses it stability by flutter;the plate undergoes limit cycle motions due to the nonlinearity after flutter instability;period-3 and period-5 motions appear along with chaotic motions;and,with the dynamic pressure increasing,divergent motions occur finally.