摘要
飞机在起飞和着陆滑跑过程中有时会遇到摆振。摆振的发生给飞机安全带来很大危害，一直以来未得到很好解决。本文以非线性动力学分岔理论为基础，应用理论分析和数值仿真相结合的方法，研究了起落架摆振建模、起落架参数的分岔分析、摆振的主动控制和半主动控制以及摆振非线性模型的分岔控制。
针对起落架扭转运动模态和侧向运动模态，建立考虑支柱侧向柔性的非线性摆振模型。提出利用基于拟弧长延拓算法的数值方法对起落架结构参数和几何参数进行分岔分析，得到摆振极限环振幅随速度的变化情况，支柱前倾角、支柱扭转阻尼、支柱扭转刚度、支柱侧向阻尼、支柱侧向刚度、机轮稳定距对系统稳定区域、扭转摆振区域以及侧向摆振区域的影响。所得结论对于起落架防摆设计具有重要指导作用。
建立具有库仑摩擦、线性项以及二次项的减摆器模型。研究表明非线性减摆器模型的摆振稳定性分析结果比线性减摆器模型分析结果更加准确，农林一机的算例结果很好的验证了非线性减摆器模型数值分析结果的准确性。运输一机的算例结果表明基于拟弧长延拓算法的数值分析方法能够比待定复参数方法得到更准确的稳定边界。提出根据摆振极限环振幅和频率特性对扭转和侧向运动模态进行划分，有助于深入认识摆振机理，时域分析和频谱图验证了所得结论的正确性。
建立主动控制的非线性摆振模型，提出利用数值延拓算法分析主动控制对摆振的抑制效果，并与被动控制进行对比。研究结果发现：相对被动控制，主动控制能有效增加系统稳定区域。利用数值延拓算法的数值分析可以指导控制参数的合理选取，达到有效抑制摆振的目标。时域分析结果与数值分析结果一致，表明本方法的有效性。提出应用直接型自适应模糊控制抑制摆振，仿真结果表明能够有效抑制参数扰动而引起的摆振。
建立应用磁流变阻尼器的起落架摆振半主动控制非线性数学模型，并设计半主动控制算法。数值分析得到半主动控制和被动控制系统稳定性分析图，研究了半主动控制对系统稳定区域、扭转摆振区域以及侧向摆振区域的影响，结果表明：基于磁流变阻尼器的半主动控制相对被动控制可以有效减小发生扭转摆振的区域。
针对非线性摆振模型，研究平方和立方非线性状态误差反馈控制对系统稳定区域、摆振区域、极限环振幅与频率的控制效果。结果表明：平方和立方非线性状态误差反馈控制可以控制扭转摆振振幅与频率，对稳定区域、摆振区域则没有控制作用。
The unwanted oscillations called shimmy can occur on both nose and main landing gears duringaircraft’s take-off or landing. The paper has studied landing gear modeling, influence of landing gearparameters, active and semi-active control of shimmy, and bifurcation control. Numerical simulationmethod based on bifurcation theory and time domain analyses are used in the research.
A nonlinear nose landing gear shimmy model is built. The model including strut lateral bending ofcharacterizes the motion of the system in terms of the torsional mode and lateral mode. Bifurcationanalysis based on pseudo arclength continuation method is used to study the stability of the systemabout landing gear structure and geometry parameters. The sensitivity of the system is studied tochanges of rake angle, torsional damping coefficient, torsional stiffness coefficient, lateral dampingcoefficient and lateral stiffness coefficient. The amplitude of shimmy changes with the forwardvelocity. The results have an important meaning to landing gear design.
A nonlinear shimmy damper model is constructed including coulomb damping，linear viscousdamping and square damping. The bifurcation diagram from nonlinear shimmy damper model is moreaccurate than bifurcation diagram from linear shimmy damper model. An example shows the accuracyof the nonlinear shimmy damper model. Another example shows more accurate stability region usingpseudo arclength continuation method. The torsional mode and lateral mode are distinguished byamplitude and frequency of limit cycles. Time domain analysis and frequency analysis verify theresults.
The numerical continuation method is proposed to analyze the effect of active shimmy control. Theresults show that active control can increase stable area in bifurcation diagram comparing withpassive control. The numerical continuation method can be used to determine the control law. Thetime domain analyses verify the effectiveness of the method. Direct fuzzy adaptive control isproposed to suppress shimmy. Simulation results show direct fuzzy adaptive control can removeshimmy vibrations caused by parameter perturbations.
Nose Landing gear with magnetorheological shimmy damper is modeled and a semi-active controllaw is designed. The bifurcation diagrams are studied about the stable area, torsional shimmy area andlateral shimmy area. The results from semi-active control are compared with passive control and showthat semi-active control of shimmy can effectively decrease torsional shimmy region.
Square and cubic nonlinear state feedback controllers are used on nonlinear shimmy model toinvestigate the controllability of shimmy amplitude, shimmy frequency, stable area and shimmy area.The results show that the controllers can control both shimmy amplitude and frequency, but have noeffects on either stable area or shimmy area.
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