直升机桨叶/吸振器系统的组合共振研究  

Helicopter blade-absorber system combination resonance research

作　　者：周薇[1] 韩景龙[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,江苏南京210016

出　　处：《振动工程学报》2015年第2期248-254,共7页Journal of Vibration Engineering

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

摘　　要：应用Lagrange方程建立了直升机桨叶/吸振器系统的非线性振动模型,将一种规范型计算方法引入到桨叶/吸振器系统的组合共振研究,分析了该系统在发生组合共振时的稳定性和局部分岔特性。利用多尺度法求出系统平均方程,并对平均方程存在一对纯虚特征值与双零特征值的两类临界情形进行了研究,得到了系统的Hopf分岔解、分岔路径以及转迁曲线,给出了初始平衡解的稳定区域。对每一种情形,理论预测结果均与Runge-Kutta验证结果完全一致。In the present paper,by using Lagrange equation,a nonlinear vibration model of helicopter blade-absorber system is established.The normal form method is introduced to the blade-absorber system for the combination resonance research,and through which,the stability and the local bifurcation characteristics of the blade-absorber system near combination resonance are analyzed.In order to derive the averaged equations,the method of multiple scales is applied,and then two kinds of critical points for the averaged equations are considered,which are characterized by a pair of purely imaginary eigenvalues and a pair of complex conjugate eigenvalues as well as a double zero eigenvalues.The Hopf bifurcation solution,bifurcation path,and tran-sition curves of the model are obtained respectively,and initial equilibrium stability region is given.For each case,the numeri-cal results obtained by Runge-Kutta method coincide with the analytical predictions.

关 键 词：非线性振动 组合共振 吸振器 多尺度法 规范型方法 

分 类 号：O322[理学—一般力学与力学基础]