一类非线性颤振问题的奇异摄动解

The Singular Perturbation Solution for a Certain Type of Nonlinear Flutter

本文将非线性振动理论中的多尺度奇异摄动法推广应用于以非定常气动力理论为基础的机翼非线性颤振分析,给出了系统颤振响应的渐近解析解,并对解的稳定性进行了分析,得到的稳定颤振边界与数值积分结果相吻合。用本文的方法对带立方型非线性刚度的颤振系统进行分析,具有既定性又定量的优点,有进一步研究的前景。

The multiple time scaling perturbation method is developed for the nonlinear flutter analysis with un-steady aerodynamics.The asymptotie analytical solution of flutter response is given and its stability is alsoanalysed.The stable flutter boundaries obtained by this approach agree well with that obtained by numeri-cal simulation.Using this method,the flutter system with cubic nonlinear stiffness can be analysed bothqualitatively and quantitatively.It is easy to apply this method to the nonlinear flutter problem of three-di-mensional wing.