Nonlinear thermal flutter of heated curved panels in supersonic air fow
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摘要: 基于von Karman 大变形理论及带有曲率修正的一阶活塞理论, 用Galerkin方法建立了超音速气流中受热二维曲壁板的非线性气动弹性运动方程; 采用牛顿迭代法计算得到由静气动载荷和热载荷引起的静气动弹性变形; 根据李雅谱诺夫间接法分析了壁板初始曲率与温升对颤振边界的影响; 对二维曲壁板的非线性气动弹性方程组进行数值积分求解,分析了动压参数对受热二维曲壁板分岔特性的影响, 给出了典型状态下曲壁板非线性颤振响应的时程图与相图. 分析结果表明对小初始曲率的曲壁板, 温升对其静气动弹性变形影响较大, 且随着温升的增加其颤振临界动压急剧减小; 对具有较大初始曲率的曲壁板, 温升对其静气动弹性变形的影响较弱, 且随着温升的增加颤振临界动压基本保持不变. 初始几何曲率与气动热效应使得曲壁板具有复杂的动力学特性, 不再像平壁板一样, 经过倍周期分岔进入混沌, 而会出现由静变形状态直接进入混沌运动的现象, 且在混沌运动区域中还会出现静态稳定点或谐波运动, 在大曲率情况下, 曲壁板不会产生混沌运动, 而是幅值在一定范围内的极限带振荡.
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关键词:
- 极限带振荡
Abstract: A nonlinear aeroelastic model for a two-dimensionalheated curved panel in supersonic air flow is established by using Galerkinmethod. The von Karman large deflection theory and the modified pistontheory appended with static aerodynamic loading are used in the formulation.The static deflection of a cylindrical curved panel is studied by numericalsimulation using Newton iterative approach. Then the stability boundarycurves under different temperature elevations are obtained by using Lyapunovindirect method. The motion equations of curved panel are solved byRunge-Kutta method, time history and phase plots of curved panel flutterresponses are depicted and corresponding bifurcation diagrams are obtainedfor better understanding of the subcritical and supercritical flutterresponses of curved panels with different initial height-rises underincreasing dynamic pressure and static thermo-aerodynamic loading (STAL).The results demonstrate that the flutter boundary drops significantly withincreasing temperature elevation for small curvature panel, whereas, theflutter boundary almost keeps the same value for large curvature panel. Theflutter dynamic behaviors of curved panels differ from those of flat panelssignificantly. Curved panels may enter chaos from static stable point whenconsidering temperature elevation effects, and static stable point and LCOmotion also exist in the chaotic motion area. For larger curvatures, chaoticmotions will not occur, however the supercritical flutter motions exhibit alimit strip oscillation in which the vibration amplitudes restrained in alimited range.-
Key words:
- limit strip oscillation
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