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通过计算受宽带噪声参激的二元机翼随机振动系统的矩Lyapunov指数,研究了系统的矩稳定和概率1稳定。首先在经典二元机翼颤振方程中加入随机激励,通过随机平均法、Girsanov定理和Feynmann-Kac公式得到关于矩Lyapunov指数的特征值问题。其次采用Fourier余弦级数对特征函数进行正交展开,得到系统矩Lyapunov指数的近似解析式。最后,通过Monte Carlo仿真验证了矩Lyapunov指数近似解析式的可信性,并讨论了系统参数、来流平均速度以及随机噪声谱密度对机翼稳定性的影响。
By calculating moment Lyapunov exponents of a two-dimensional wing random vibration system driven by wideband noise, the moment stability and the probability 1 stability of the system are studied. Firstly, we add stochastic excitation to the flutter equation of classical binary wing, and then obtain the eigenvalue problem of Moment Lyapunov exponents by means of stochastic averaging, Girsanov’s theorem and Feynmann-Kac formula. Secondly, using the Fourier cosine series to orthogonalize the eigenfunctions, an approximate analytic formula of the Lyapunov exponent of the system is obtained. Finally, the Monte-Carlo simulation verifies the credibility of approximate Lyapunov exponent analytic formula, and discusses the influence of system parameters, average velocity of incoming stream and random noise spectral density on wing stability.