超音速气流中受热曲壁板的非线性颤振特性

NONLINEAR THERMAL FLUTTER OF HEATED CURVED PANELS IN SUPERSONIC AIR FOW

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.

A nonlinear aeroelastic model for a two-dimensional heated curved panel in supersonic air flow is established by using Galerkin method.The von Karman large deflection theory and the modified piston theory appended with static aerodynamic loading are used in the formulation.The static deflection of a cylindrical curved panel is studied by numerical simulation using Newton iterative approach.Then the stability boundary curves under different temperature elevations are obtained by using Lyapunov indirect method.The motion equations of curved panel are solved by Runge-Kutta method,time history and phase plots of curved panel flutter responses are depicted and corresponding bifurcation diagrams are obtained for better understanding of the subcritical and supercritical flutter responses of curved panels with different initial height-rises under increasing dynamic pressure and static thermo-aerodynamic loading（STAL）.The results demonstrate that the flutter boundary drops significantly with increasing temperature elevation for small curvature panel,whereas, the flutter boundary almost keeps the same value for large curvature panel.The flutter dynamic behaviors of curved panels differ from those of flat panels significantly.Curved panels may enter chaos from static stable point when considering temperature elevation effects,and static stable point and LCO motion also exist in the chaotic motion area.For larger curvatures,chaotic motions will not occur,however the supercritical flutter motions exhibit a limit strip oscillation in which the vibration amplitudes restrained in a limited range.