基于最大李雅普诺夫指数的壁板热颤振特性分析

文章介绍了李雅普诺夫指数的定义,给出了壁板热颤振特性分析模型,计算得到超声速气流中受热壁板的非线性颤振运动形态以及相应的最大李雅普诺夫指数,画出了壁板稳定性区域图,结果显示不同参数下,超声速气流中受热壁板具有包括颤振在内的5种不同性质的振动形态:收敛于平壁板平衡点的衰减振动、收敛于屈曲平衡点的衰减振动、简谐型极限环颤振、非筒谐周期型极限环颤振和混沌型颤振,并给出了各种振动形态典型的时程响应图、相轨迹以及对应的最大李雅普诺夫指数.分析结果表明,来流速压和温升都严重影响着受扰壁板的非线性振动响应特性,壁板颤振容易发生在来流速压较大或者温度较高的参数区域,系统的最大李雅普诺夫指数能够定量表征壁板稳态响应时的运动形态,可以用该指数来判断超音速气流中受热壁板的稳定性并确定所研究参数范围内壁板的稳定性边界.

Analysis of Panel Thermal Flutter Using Maximum Lyapunov Exponent

We build the nonlinear aeroelastic model for a two-dimensional heated panel and introduce the maximum Lyapunov exponent to determine the character of the nonlinear motion of the heated panel under various aerodynamic pressures and temperature rises.Section 1 of the full paper briefs the Lyapunov exponent.Subsection 2.1 explains how to obtain the stability region of the heated panel through using the response phase plot of the motion of the heated panel together with its maximum Lyapunov exponent.Subsection 2.2 gives the numerical results and their discussion.Figs.1 and 2 present the deflection time history and phase plot of decay vibration converging respectively to:(1)the initially static equilibrium;(2)a post buckling equilibrium.Figs.3 and 4 give the defleetion time history,phase plot and final stable state LCO(1imit cycle oscillation)phase plot respectively of:(1) simple harmonic LCO flutter;(2)periodic but not simple harmonic LCO flutter.Fig.5 shows the deflection time history and phase plot of chaotic flutter.Fig.6 and Table 1 present respectively the stability regions and the maximum Lyapunov exponents of the heated panel under various aerodynamic pressures and temperature rises.