EI、Scopus 收录
中文核心期刊

宽带噪声作用下黏弹性板的矩Lyapunov指数

On the moment lyapunov exponent of a viscoelastic plate subjected to the excitation of wide band noises

  • 摘要: 主要研究了在超音速流中受宽带噪声作用的黏弹性板随机振动系统的矩Lyapunov指数.首先, 采用vonKarman板弯理论, 活塞理论以及Galerkin近似法建立了两个自由度耦合的系统运动的随机微分方程. 其次, 应用随机平均法将四维系统降为二维系统. 接着, 对系统采用极坐标变换,通过Girsanov定理和Feynmann-Kac公式得到后向微分算子. 通过对特征函数进行正交Fourier余弦级数展开得到系统矩Lyapunov指数的近似解析式. 并通过MonteCarle仿真得到系统矩Lyapunov指数的数值解验证了近似解析式的可信性. 最后研究了系统参数、气动力参数以及随机噪声谱密度对黏弹性板稳定性的影响.

     

    Abstract: In the present paper, the moment Lyapunov exponent of aviscoelastic plate in a supersonic gas flow subjected to the excitation ofwide band noises is investigated. A aeroelastic model for two coupleddegrees-of-freedom panel is established by using the Von Karman platestheory, the quasi-first-order piston theory and Galerkin approximation. Viathe stochastic averaging method, the four-dimensional system is reduced to atwo-dimensional one. Through the logarithmic polar transformation , and thenGirsanov theorem and Feynmann-Kac formula, the backward differentialoperator is then obtained. By expanding the eigenfunctions as a Fouriercosine series, the approximate analytic expansion of the moment Lyapunovexponent is then obtained and matched by the Monte Carle simulation results.Finally, the influences of the system parameters, gas dynamical parametersand the spectral density of noises on the stochastic stability ofviscoelastic plate is studied.

     

/

返回文章
返回