基于分岔理论的直升机地面共振分析

Investigation of Helicopter Ground Resonance Based on Bifurcation Theory

基于拉格朗日法建立了旋翼/机体耦合的直升机地面共振动力学模型,该模型考虑了非线性桨叶摆振阻尼的影响。采用非线性分岔理论对无阻尼地面共振动力学系统的自激振动边界进行了预测,并与经典的Cloeman特征方程法得出的结果进行了对比验证。随后利用该理论分析了无阻尼及含桨叶非线性摆振阻尼的地面共振系统的动力学特性。结果表明,采用非线性桨叶摆振阻尼使地面共振动力学系统在自激振动区域呈现出有限幅度的极限环振动,同时也避免了系统在该区域运动发散,且极限环振动幅值与非线性阻尼相关。

Based on the Lagrangian method,the coupled rotor/fuselage ground resonance model is presented,considering the effect of nonlinear blade lag damping.The nonlinear bifurcation theory is applied to the boundary prediction of self-excited oscillation zone of non-damping ground resonance dynamic system.And the validation of the system is presented with the result of classic Coleman characteristic equation method.The nonlinear bifurcation theory is also used to investigate the dynamic behaviors of ground resonance systems with blade lag and without damping.It is shown that the system containing the blade lag damping proceeds the limit cycle oscillation（LCO） and avoids the motion divergence in self-excited oscillation zone.Moreover,the amplitude of LCO is related to the nonlinear damping.