考虑结构刚度不确定性的概率颤振分析

针对舵面颤振系统中存在的不确定性问题，考虑参数的随机分布，利用蒙特卡罗模拟（MCS，Monte Carlo Simulation）和非浸入式随机多项式（NIPC，Non-Intrusive Polynomials Chaos）两种方法进行概率颤振分析，以对结构稳定性和颤振风险进行评估.选取一个存在非线性因素的典型三维舵面作为研究对象，考虑舵机弯曲刚度和扭转刚度两个不确定性变量均满足高斯分布，基于MCS和NIPC两种方法开展不确定性定量分析工作.MCS方法选取大量的样本进行颤振计算，而随机多项式方法利用配点法建立代理模型，以此获得大量的颤振信息，进而得到舵面系统发生颤振的危险速度区域及给定速度下系统发生颤振的概率，并对两种方法的置信水平、计算精度和计算效率进行了比较分析.结果表明，以不确定性量化为基础的概率颤振分析方法能充分利用不确定参数的概率信息对结构系统的颤振风险做出评定. 

Probabilistic flutter analysis with uncertainties in structural stiffness

A probabilistic flutter analysis method was proposed to evaluate the structural stability and flutter risk of the rudder, which was subject to uncertainties in structural parameters with stochastic distribution. Monte Carlo simulation (MCS) and non-intrusive polynomials chaos (NIPC) method were used. A typical 3-D rudder with nonlinear factors, whose steering gear has two uncertain variables, that is bending rigidity and torsional rigidity, both satisfying Gauss distribution, was selected to examine the present method. A large amount of flutter information was obtained by flutter calculations of massive samples when using the MCS method, while which was gotten by surrogate models with point-collocation method when using the NIPC method. After that, the dangerous regions of velocity and the probability of flutter under certain velocity were obtained. Then the comparisons of the confidence level, analytic precision and efficiency of calculation were conducted. The results suggest that the probabilistic flutter analysis method based on uncertainty quantification is effective in the flutter risk assessment of structures using the probability information of the uncertain parameters.