振荡激波作用下壁板的非线性动力学特性分析
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O322;V215.3

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国家自然科学基金资助项目(11732013);国家数值风洞项目(NNW2019ZT3-A15)


Nonlinear dynamic analysis of a panel subjected to oscillating oblique shock
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    摘要:

    冲压发动机内部的激波串往往存在振荡特征,揭示此种状态下壁板的气动弹性特性对结构安全性具有重要指导作用。基于von Kármán 大变形理论和当地一阶活塞流理论,采用Galerkin 方法建立了振荡激波作用下壁板的非线性动力学方程,通过龙格?库塔法对非线性动力学方程进行数值积分求解,在不同的系统参数(即激波强度、激波振荡幅值以及振荡频率)下,取来流动压为分岔参数,研究壁板在振荡激波作用下的分岔及混沌等复杂动力学特性。计算结果表明:与激波位置固定情况相比,壁板在振荡激波作用下表现出更加丰富的动力学行为,其分岔特性更加复杂。极限环幅值随着激波强度和振荡幅值的增大而增大。激波的振荡容易激发出混沌运动,并且通往混沌的道路为准周期道路。激波强度的增大不会改变通往混沌的道路,而当激波振荡幅值大幅度提高时,不仅混沌区域显著增大,通往混沌的道路不再是准周期道路,而是经历更为复杂的过程进入混沌。

    Abstract:

    The shock trains in ramjet/scramjet are generally oscillatory. Thus,study of aeroelastic characteristics of the panel subjected to the oscillating shock has important guidance to the structural safety. Based on Von-Kármán large deflection plate theory and local first-order piston theory,the nonlinear dynamic equations of the panel subjected to an oscillating oblique shock are established by using the Galerkin discrete method. The fourth-order Runge-Kutta numerical integration method is adopted to solve the nonlinear dynamic equations. Considering different system parameters(i.e. shock strength,oscillation amplitude and oscillation frequency of the shock)and taking dynamic pressure as bifurcation parameter,the bifurcation characteristics and chaos behaviors of the panel subjected to an oscillating oblique shock are studied. The results show that compared with the case in which the shock location is fixed,the dynamic behaviors of the system are richer and the bifurcation characteristics are more complex when the panel is subjected to an oscillating shock. The LCO amplitude is observed to increase with the shock strength and oscillation amplitude of the shock. Under the action of the oscillating shock,chaotic motion is very easily excited and the route to the chaotic motion is via the quasi-periodic motion. The increase of the shock strength will not change the route to the chaotic motion. However,when the oscillation amplitude of the shock is significantly increased,the route to the chaotic motion is no longer via the quasi-periodic motion but a more complex process.

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叶柳青,叶正寅.振荡激波作用下壁板的非线性动力学特性分析[J].振动工程学报,2022,35(2):464~474.[YE Liu-qing, YE Zheng-yin. Nonlinear dynamic analysis of a panel subjected to oscillating oblique shock[J]. Journal of Vibration Engineering,2022,35(2):464~474.]

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  • 在线发布日期: 2022-05-31
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