Dryden大气紊流频谱的等价确定性函数及其在飞机响应问题中的应用

本文扼要评述了B.Etkin等人最近发表的多输入随机过程的等价确定性输入方法（EDIT）,并且加以扩展,导出线性变换公式,分析了确定性输入函数的奇偶性。按照EDIT把目前常用的Dryden大气紊流频谱化成等价确定性时间函数,并拟合成简单的表达式。说明了在时域内计算飞机对大气紊流响应特性的方法和步骤。在算例中比较了用EDIT和常规的功率频谱法所得的结果。

THE EQUIVALENT DETERMINISTIC FUNCTION OF THE DRYDEN'S SPECTRA OF ATMOSPHERIC TURBULENCE AND ITS APPLICATION TO THE AIRCRAFT RESPONSE PROBLEM

The equivalent deterministic input technique （EDIT） for multi-input-random process published recently by B. Etkin, P. Hughes and S. Zhu is first reviewed briefly in this paper. Then a formula of linear transformation （Eqs. 7,8） is derived and the singularity of the equivalent input function is shown（Eq. 9）. By analysing the characteristics of the turbulence spectral maxtrix （Eq. 11） for the longitudinal motion of an aircraft, including two gust velocities and one gust gradient, it turns out that only two （rather than three） equivalent input vectors are needed （Eq.15）.The Dryden's spectra of atmospheric turbulence in current use （Eq. 14） are decomposed into U11, U22, U33, and the inversed Fouriertransform is performed subsequently （Eq. 3） to obtain the equivalent deterministic input function u11, u22, u32 （ = uE32 + uO32） （Figs.1, 2） for the reference flight condition. These curves are then fitted by simple expressions （Eq. 16）. The method and procedure for numerical computation or simulation of the aircraft response to turbulence in the time domain are proposed and discussed（Eqs. 18, 20, 21）. A numerical example is given for comparing the results from EDIT and PST （power spectral technique） （Table 1）.