振荡激波作用下受热壁板主共振特性分析  

Analysis of primary resonance characteristics of heated wall plate under oscillating shock wave

作　　者：叶柳青 叶正寅[1] 洪正 叶坤[1] YE Liuqing;YE Zhengyin;HONG Zheng;YE Kun(School of Aeronautics,Northwestern Polytechnical University,Xi’an 710072,China)

机构地区：[1]西北工业大学航空学院,西安710072

出　　处：《振动与冲击》2022年第9期41-50,共10页Journal of Vibration and Shock

基　　金：国家自然科学基金(11732013)。

摘　　要：冲压发动机内部的激波串往往存在振荡特征,研究振荡激波作用下受热壁板的主共振特性对结构安全性具有重要指导作用。基于Von-Karman大变形理论和当地活塞流理论,采用Galerkin方法建立了振荡激波作用下壁板振动的动力学模型,通过龙格-库塔法对非线性动力学方程进行数值计算获得系统非线性振动响应,发现受热壁板在振荡激波作用下存在振动突跳和双稳态现象等典型的非线性动力学行为,并分析了振荡激波强度、激波振荡幅值、温度、激波振荡的中心位置、来流马赫数对系统振动突跳和双稳态特性的影响。结果表明:随着振荡激波强度、激波振荡幅值和来流马赫数增大,系统共振峰值不断单调增大,而双稳态区间由不存在先变宽、再变窄直至消失,然后再急剧变宽;温度增大会对系统产生“刚度弱化效应”;将激波振荡的中心位置向壁板两端移动可有效地降低系统共振峰值并抑制振动突跳和双稳态现象。Shock wave trains in ramjets often has oscillation characteristics.Studying primary resonance characteristics of heated wall plate under the action of oscillating shock wave plays an important guiding role on structural safety.Here,based on Von-Karman large deformation theory and the local piston flow theory,the dynamic model of a wall plate under oscillating shock wave was established using Galerkin method.Nonlinear dynamic equations were numerically calculated with Runge-Kutta method to obtain the system’s nonlinear vibration responses.It was shown that the heated wall plate has typical nonlinear dynamic behaviors,such as,vibration jump and bi-site phenomenon phenomena under the action of oscillating shock wave.Effects of oscillating shock wave intensity,shock wave oscillation amplitude,temperature,shock wave oscillation center position and incoming flow Mach number on the system’s vibration jump and bi-stability were analyzed.The results showed that with increase in oscillating shock wave intensity,shock wave oscillation amplitude and incoming flow Mach number,the system resonance peak value increases monotonically,while the bi-site phenomenon interval firstly appears and widens,then narrows until it disappears,and then widens sharply;increase in temperature can produce"stiffness weakening effect"on the system;moving center position of shock wave oscillation to both ends of wall plate can effectively reduce the system resonance peak value and suppress vibration jump and bi-site phenomenon phenomena.

关 键 词：振荡激波 主共振 当地活塞流理论 振动突跳 双稳态 非线性振动 

分 类 号：O322[理学—一般力学与力学基础] V215.3[理学—力学]