| 吴杰,王志东,虞志浩.精细时程积分法及其数值衍生格式应用评估[J].计算力学学报,2019,36(1):132~137 |
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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：2017-11-27 |
| DOI：10.7511/jslx20170926002 |
| 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 precision direct scheme trapezoidal method |
| 基金项目:国家自然科学基金（51679114）资助项目. |
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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，精细积分法对矩形直桨叶动力学方程具有足够的求解精度。 |
| 英文摘要: |
| Helicopter rotor aeroelasticity is essentially described by 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 blades.This paper introduces a precise time integration method (PTI) and its derived formats to solve this kind of equations.The Duhamel integration term in the derived formats can be calculated using this 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,an implicit integration method is used to comprehensively evaluate PTI on rotor dynamics.Numerical examples indicate that HPD scheme is precise evough to be used for rectangular blades. |
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