一种消除非线性振动摄动解中奇异项的方法及其应用

New Perturbation Solution of Nonlinear Vibration of Aircraft Nosewheel Shimmy System

提出了一种消除非线性振动摄动解中奇异项的有效方法——特征矩阵三角分解法，与其它消除奇异项的方法相比，该方法具有运算量少、易于操作等优点。应用该方法求出了具有速度平方阻尼的飞机前轮非线性摆振系统的摄动解，验证了方法的正确性，并改正了有关文献的错误。

Secular terms, unavoidable in perturbation solutions of nonlinear vibration problems, are quite a nuisance. Our new method can effectively eliminate these terms through a special mathematical technique developed by us. We decompose the characteristic matrix of the nonlinear vibration system, and use the singularity properties of the characteristic matrix when the vibration system is critically stable; secular terms can be eliminated if eq.(10), a matrix equation, can be solved; eq.(10) can be sloved if eq.(17) is satisfied; in fact eq.(17) is easily satisfied. So the elimination of secular terms is straightforward. We give the perturbation solutions of aircraft nosewheel shimmy system that includes velocity squared damping, which prove that our method is effective.