活塞理论非线性项对壁板颤振特性的影响研究

Effect of nonlinear terms in piston theory on characteristics of panel flutter

目前,活塞理论非线性项对壁板颤振的影响规律尚未得到系统性总结。基于一、二、三阶活塞理论建立了超声速气流下的二维简支非线性壁板颤振的运动方程。应用李雅普诺夫间接法分析受热简支壁板的稳定性,基于数值分析法对壁板颤振方程进行数值求解,研究活塞理论非线性项对壁板颤振的影响规律。结果表明:①在小温升比下,一阶活塞理论下壁板响应仅表现为收敛运动和单周期极限环颤振,而高阶活塞理论下,壁板响应表现更为复杂,除了上述特征之外,还存在多周期极限环颤振和混沌运动等更加复杂的非线性动力学现象;②随着马赫数的增加,一阶活塞理论和高阶活塞理论下的壁板动态响应出现显著差异时所需的动压和温升比逐渐减小;③在高马赫数与较高动压下,二阶活塞理论和三阶活塞理论的计算结果出现显著差异,同时在高温升比下,也会出现相同的现象;④当壁板动态响应特征基本一致时,高阶活塞理论计算的位移响应峰值通常小于一阶活塞理论计算结果,最大误差可达到约16.66%。文中研究结果对于实际工程应用中在不同条件下如何选择适用的简支壁板颤振分析方法具有一定参考价值。

Currently,there is no systematic summary of the influence of the nonlinear terms in piston theory on the panel flutter.The two-dimensional nonlinear panel flutter equations under supersonic airflow based on the first,second,and third-order piston theories is established.The stability of the heated panel is analyzed by using the Lyapunov′s indirect method,and the panel flutter equations are numerically solved based on the numerical analysis method to investigate the influence of the nonlinear terms in piston theory on the panel flutter.The results show that:①Under a small temperature rise ratio,the panel response under the first-order piston theory only exhibits the convergent motion and single-period limit cycle flutter.While under higher-order piston theories,the panel response is more complex,exhibiting more complex nonlinear dynamic phenomena such as multi-period limit cycle flutter and chaotic motion in addition to the aforementioned characteristics.②As the Mach number increases,the required dynamic pressure and temperature rise ratio decrease gradually when the dynamic response of the panel under the first-order piston theory and higher-order piston theories exhibit significant differences.③The significant differences in the computational results of the second-order and third-order piston theory appear under the high Mach numbers and relatively high dynamic pressures,and the same phenomenon occurs underthe high temperature rise ratios.④When the dynamic response characteristics of the panel are basically consistent,the displacement response peak calculated by using the higher-order piston theory is usually smaller than the result calculated by using the first-order piston theory,and the maximum error can reach about 16.66%.The present results have certain reference value for selecting the appropriate analysis method for the panel flutter under different conditions in practical applications.