Grazing bifurcation in aeroelastic systems with freeplay nonlinearity
Grazing bifurcation in aeroelastic systems with freeplay nonlinearity
复制标题
DOI：
10.1016/j.cnsns.2013.09.022
复制
发表时间：
2014-05
期刊：
影响因子：
--
通讯作者：
R. Vasconcellos;A. Abdelkefi;M. Hajj;F. Marques
中科院分区：
文献类型：
--
作者：
R. Vasconcellos;A. Abdelkefi;M. Hajj;F. Marques
为了研究非光滑间隙非线性对气动弹性系统响应的影响，进行了非线性分析。该系统由一个在纵倾自由度上由一个线性弹簧支撑的、在俯仰自由度上由一个非线性弹簧支撑的、具有纵倾和俯仰运动的刚性机翼组成。非光滑间隙非线性与俯仰自由度有关。气动载荷采用非定常公式建模。首先进行线性分析以确定耦合阻尼和频率以及相关的线性颤振速度。然后，进行非线性分析，以确定间隙的大小对气动弹性系统的响应的影响。为此，考虑两种不同的尺寸。结果表明，对于两种间隙，当自由振动速度（低于线性颤振速度）变化时，系统响应会出现两种不同的过渡或突变，即由不连续性引起的二次非线性的出现和消失。它表明，这些突然的过渡与轨迹和自由间隙边界（掠分叉）之间的切向接触。在第一个过渡，它表明，增加的自由速度是伴随着出现的超谐波频率的主振荡频率的2阶。在第二个过渡，结果表明，在自由振动速度的增加，其次是2阶的超谐波频率的消失，并返回到一个简单的周期性响应（主振荡频率）。
A nonlinear analysis is performed to characterize the effects of a nonsmooth freeplay nonlinearity on the response of an aeroelastic system. This system consists of a plunging and pitching rigid airfoil supported by a linear spring in the plunge degree of freedom and a nonlinear spring in the pitch degree of freedom. The nonsmooth freeplay nonlinearity is associated with the pitch degree of freedom. The aerodynamic loads are modeled using the unsteady formulation. Linear analysis is first performed to determine the coupled damping and frequencies and the associated linear flutter speed. Then, a nonlinear analysis is performed to determine the effects of the size of the freeplay gap on the response of the aeroelastic system. To this end, two different sizes are considered. The results show that, for both considered freeplay gaps, there are two different transitions or sudden jumps in the system’s response when varying the freestream velocity (below linear flutter speed) with the appearance and disappearance of quadratic nonlinearity induced by discontinuity. It is demonstrated that these sudden transitions are associated with a tangential contact between the trajectory and the freeplay boundaries (grazing bifurcation). At the first transition, it is demonstrated that increasing the freestream velocity is accompanied by the appearance of a superharmonic frequency of order 2 of the main oscillating frequency. At the second transition, the results show that an increase in the freestream velocity is followed by the disappearance of the superharmonic frequency of order 2 and a return to a simple periodic response (main oscillating frequency).