导　　师： 刘勇

学科专业： 082502

授予学位： 硕士

作　　者： ;

机构地区： 南京航空航天大学

摘　　要： 直升机旋翼气弹响应积分是气弹稳定性分析以及振动载荷预估的基础,气弹综合分析模型是典型的非线性周期时变系统,求解十分复杂。目前常用的直接积分法如Newmark法、HHT法等在精度和稳定性方面均不理想,算法的系统误差可能引起数值震荡、发散或耗散,使气弹响应积分解难以收敛,难以得到稳态解。 本文基于精细积分法,重点针对旋翼气弹系统的非线性以及周期时变特点,设计了高阶精度的精细积分算法。首先,基于一次Jacobi重构,构造了包含全部高阶截断误差的等价系统,把原系统分解为线性定常部分、时变部分和非线性部分;然后,以线性定常部分的精确积分为基础,把微分方程中时变部分和非线性部分的求解转化为积分方程的杜哈梅尔向量积分;最后利用指数矩阵核函数的性质,构造了任意阶精度的向量积分格式,其中在积分步长内构造了高斯点的三次多项式预估格式,而一次Jacobi矩阵采用了割线修正。同时进行了算法的稳定性分析。 为了验证算法的有效性,本文开展了大量的数值计算研究,通过对比验证表明,该算法能有效地求解非线性时变动力系统,响应计算的精度、稳定性、计算效率等方面均优于目前通用的差分类算法,能够有效的应用到直升机旋翼气动弹性响应的数值积分中。 Helicopter rotor aeroelastic response numerical integration is the basis for stability analysis and dynamic load prediction. Rotor aeroelastic comprehensive analysis model is a typical non-linear and periodic time-varying systems which solution procedure is very complicated. The most commonly used methods such as direct integration Newmark method, HHT law etc are not gratifying in the accuracy and stability, which may cause inaccurate results by reason of numerical oscillation, dispersion, or dissipation of difference schemes. Frequently, it is very difficult to achieve convergent steady state aeroelastic response solutions. Based on the high-precision integration method/(HPIM/), a modified and much more precise HPIM scheme/(3M-HPIM/) is designed by well accounting for the nonlinear and time-varying characteristics of rotor aeroelastic model. Firstly, using the low order Jacobi reformation technique, the original system is reformed to three parts: the linear autonomy system, the time-varying system, and the nonlinear system, withholding all high trunction errors. And so, this reformation is Jacobi equivalent to original system. Then, the time-varying and the nonlinear parts are transformed from the non-homogeneous terms of differential eguation to the Duhamel integral representation of integral equation. And last, according to the properties of exponential matrix kernel function, this study has developed a arbitrary precision Gaussian numerical integration algorithm for the Duhamel integral, and with necessarily Gaussian points forecasting by threetimes polynomial approximation. To verify the effectiveness of this 3M-HPIM numerical integraton scheme, sufficient numerical trials, including strong nonlinear and quickly time-varying systems, have been test and validated. This study finally well verified the effectiveness of 3M-HPIM numerical integraton scheme, with much more precise and more stabile than the most commonly used difference schemes.

关 键 词： 直升机 旋翼气弹响应 精细积分 非线性动力系统 周期时变 直接积分

领　　域： [航空宇航科学与技术]