#  ## MATLAB精细时程积分法在旋翼动力学方程求解中的应用

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

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

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