基于切比雪夫多项式的旋翼响应及稳定性  

Rotor Response and Stability Based on Chebyshev Polynomials

作　　者：周薇[1] 韩景龙[1] 陈全龙[1] 

机构地区：[1]南京航空航天大学机械结构力学及控制国家重点实验室,南京210016

出　　处：《南京航空航天大学学报》2013年第5期628-632,共5页Journal of Nanjing University of Aeronautics & Astronautics

基　　金：高等学校博士学科点专项科研基金(20113218110002)资助项目;江苏高校优势学科建设工程资助项目

摘　　要：根据Hamilton原理,采用准定常气动力模型,建立直升机旋翼的有限元方程,利用移位的第一类切比雪夫多项式计算了旋翼的周期响应。在分析周期响应的稳定性时,通过移位的第一类切比雪夫多项式的积分运算,能够快速准确地求得旋翼系统的Floquet转移矩阵。算例显示,本方法所得的解析周期响应与时间有限元法所得数值解吻合良好,稳定性分析准确且无需借助Hsu法等数值方法,验证了将切比雪夫多项式理论引入到直升机气弹响应研究的可行性和正确性。According to the Hamilton principle,using quasi-steady aerodynamic model,the finite element equations of the helicopter rotor are established,and the periodic responses of rotor can be calculated via the shifted Chebyshev polynomials of the first kind.In the stability study of periodic responses,the Floquet transition matrix can be obtained quickly and accurately by the integral operation of shifted Chebyshev polynomials of the first kind.The example shows that the analytic periodic responses obtained by the suggested method coincide with the numerical solutions obtained by the time finite element method,and the stability analysis is accurate without the help of any other numerical approach such as Hsu method.It is proved that Chebyshev polynomials theory brought into aeroelastic response research area is viable and correct.

关 键 词：非线性动力学 移位的第一类切比雪夫多项式 近似解析解 稳定性 

分 类 号：V211.52[航空宇航科学与技术—航空宇航推进理论与工程]