泛函级数在导弹主翼振动分析上的应用

为了研究突风载荷对导弹主翼的垂直振动及俯仰倾角的影响,提出了对非线性动态系统做建模研究的Voherra泛函方法的任意高阶核估计方法.该方法在核理论基础上,构造线性空间,将求解Volterra泛函各阶核的问题转化为求输出观测向量在希尔伯特空间子空间上的分量,利用线性空间中向量内积的求解而间接辨识出复杂的非线性动态系统.相对于其他在时域或频域估计Volterra核的理论,该方法数学基础清晰、计算量不随辨识精度增高而增加、能够对任意高阶核进行估计,可对强非线性动态系统进行辨识,回避了计算量很大的计算流体力学(CFD).虽然对模型的喂给数据量有一定要求,但与随机和伪随机信号的随机响应法、Lee-Schetzen法和其他的统计量辨识方法比较,不需要对喂给数据量和概率分布有太高要求.通过该方法辨识出来的各阶核,可以立即得到系统的一阶幅相频响应和各阶广义频率响应.在NACA64-008A翼型加载线性扫频调幅拉伸力,将系统响应与辨识模型响应及Ijee-Schetzen法在不同喂给数据量下辨识结果做了对比和说明.

Application of Functional Series to Vibration Analysis of Missile Aerofoil

To evaluate the plunge and pitch motion of a two-dimensional missile aerofoil exposed to gust as well as influenced by a high speed stream, a model of the aerofoil is established. Volterra functional series are used to analyze the nonlinear dynamic aeroelastic aerofoil system. An accurate and efficient algorithm to identify an arbitrary order of Volterra kernel is put forward. The results from a generalized Fock space, one kind of repro-duced kernel Hilbert spaces, are made use of to compute the Volterra functional kernels. Nonlinear aeroelastic kernels are obtained. Time histories of experiments and the model's predictive results are compared. In the frequency domain, first and second order frequency responses of the experiments and the simulation results of the model are also compared, and the error is found to be acceptable. Vibration response of the aerofoil excited with chirp signal loads is analyzed during experiments. The results agree with the model prediction. Our model is compared with the Lee-Schetzen model, which shows that our model can use fewer experimental data to a-chieve better approximation. Highly nonlinear dynamic systems can be modeled with this method. It can be used on an aeroelastic dynamic system while avoiding burdensome computational fluid dynamics.