MATLAB精细时程积分法在旋翼动力学方程求解中的应用

摘要旋翼动力学研究对象是直升机旋翼桨叶和桨毂，其主要包括三大部分：频率、响应与振动。其中振动研究又建立在动响应计算的基础之上。所以旋翼动力学动响应计算（即动力学微分方程的求解）精度决定着旋翼桨叶、桨毂振动分析的精度。旋翼动力学方程主要描述对象是桨叶构件，而桨叶本身具有结构预扭、变截面以及特殊桨尖布局等特性。所以方程中结构与几何非线性较强，自由度耦合较复杂。这些特性进一步造成了桨叶有限元划分单元数较多、方程规模较大的问题。由于桨叶始终处于离心力场中，方程中将同时含有轴向拉伸和弹性扭转自由度。桨叶在这两个方向上的较大刚度差异直接导致了微分方程的刚性较大。鉴于上述原因，旋翼动力学方程具有较强非线性、较大刚性比的特征。因此提高这类方程的求解精度便成了动力学研究中的关键问题之一。传统求解方法往往采用模态截断法，且只针对充分简化的结构动力学方程。本课题引入精细时程积分法尝试求解旋翼动力学这类方程。本课题首要任务是理解经典的精细时程积分法及其衍生方法，优选其中精度实现较高的方法应用于微分方程求解。其次是利用MATLAB程序将该方法与四阶Runge-Kutta法等作深入比较，目的是研究它们在积分精度、收敛速度以及数值稳定性等方面的特点。79122

毕业论文关键词：旋翼动力学；非线性系统；精细时程积分；算法比较

Abstract Rotor dynamics research objects are helicopter rotor blades and the hub, it mainly includes three parts: frequency, response and vibration。 The vibration research is based on the dynamic response calculation。 So the rotor dynamic response calculation accuracy (i。e。 solving dynamics differential equations) accuracy determines the rotor hub vibration analysis。 Rotor dynamic equations mainly describe the object is the blade member, and the blade itself with the structure of pre-twisted, variable cross-section and special blade tip layout and other characteristics。 So the structure and geometry of the equation are strong, and the degree of freedom coupling is more complex。 These characteristics result in a larger number of finite element units and the equations。 The blade is always in a centrifugal force field, therefore，the equation will contain both axial tension and elastic torsion freedom。 The large stiffness of the blade in these two directions directly leads to the rigidity of the differential equation。 In view of the above reasons, the rotor dynamics equation has the characteristics of strong nonlinearity and large stiffness ratio。 So it is one of the key problems in the study of dynamics to improve the solution accuracy of this kind of equations。 The traditional solution method often uses the modal truncation method, and only the structure dynamics equation is simplified。 The precise time integration method is introduced in this paper to solve the equations of rotor dynamics。 The primary task of this paper is to understand the classical precise time integration method and its derivative method, and to optimize the accuracy of the method to solve the problem。 Secondly, this method is compared with the four order Runge-Kutta method by using MATLAB program。 The aim is to study the characteristics of convergence speed, numerical stability and integral precision。

Keywords: rotor dynamics; nonlinear system; precise time integration; comparison of algorithms

第一章绪论 1

1。1 研究背景 1

1。2 旋翼动力学综述 2

1。2。1 旋翼运动特点 2

1。2。2 旋翼动力学结构 MATLAB精细时程积分法在旋翼动力学方程求解中的应用:http://www.youerw.com/wuli/lunwen_91371.html