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精细时程积分法及其数值衍生格式应用评估
REVIEW ON PRECISE TIME INTEGRATION METHOD AND ITS DERIVED FORMATS
投稿时间:2017-09-26  修订日期:2017-10-27
DOI:
中文关键词:  旋翼动力学  偏微分方程  精细积分法  高精度直接积分法  梯形方法
英文关键词:rotor dynamics  partial differential equation  precise time integration method  high precise direct scheme  trapezoidal method
基金项目:国家自然科学基金项目(面上项目,重点项目,重大项目)
作者单位E-mail
吴杰 江苏科技大学 stephenwu@163.com 
王志东 江苏科技大学  
虞志浩 南京航空航天大学  
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中文摘要:
      旋翼气动弹性耦合动力学方程本质上是一组刚性比较大的非线性偏微分方程。在有限元结构离散后,可改写为非齐次微分方程组,其中非齐次项是桨叶运动量(位移与速度)和气动载荷的函数。针对这类方程,本文尝试引入精细积分法及其衍生格式,借助数值方法计算Duhamel积分项。从积分精度与数值稳定性方面,比较研究具有代表性的精细库塔法和高精度直接积分法。结合隐式积分算法,评估精细积分法应用于旋翼动力学方程的可行性。算例表明,精细积分法对于矩形直桨叶动力学方程求解精度是足够的。
英文摘要:
      Description of helicopter rotor aeroelasticity is essentially a set of stiff and nonlinear partial differential equations. They can be rewritten as non-homogeneous ordinary differential equations after discretion by finite element method. The non-homogeneous terms depend on time response and aerodynamic loads of the blade. This paper introduces precise time integration method (PTI) and its derived formats to solve this kind of equations. As in derived formats, Duhamel integration term in PTI can be calculated using numerical method. It also selects and compares the precise-Kutta method and high precision direct scheme (HPD) on integration precision and numerical stability. At last, implicit integration method is involved to comprehensively review PTI on rotor dynamics. Numerical examples indicate that HPD scheme is precise enough to be used for rectangular blades.
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