CAJ | 학술논문

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。
응용 Lagrange 방정건립료직승궤장협/흡진기계통적비선성진동모형，장일충규범형계산방법인입도장협/흡진기계통적조합공진연구，분석료해계통재발생조합공진시적은정성화국부분차특성。이용다척도법구출계통평균방정，병대평균방정존재일대순허특정치여쌍령특정치적량류림계정형진행료연구，득도료계통적 Hopf 분차해、분차로경이급전천곡선，급출료초시평형해적은정구역。대매일충정형，이론예측결과균여 Runge-Kutta 험증결과완전일치。
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.