振荡激波作用下受热壁板主共振特性分析

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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，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。本文基于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。

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	叶柳青
	叶正寅
	洪正
	叶坤

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

Abstract：The shock trains in ramjet/scramjet are generally oscillatory, thus study of primary resonance characteristics of heated panel subjected to an oscillating oblique shock has important guidance to the structural safety. Based on Von-Karman large deflection plate theory and local first-order piston theory, the nonlinear dynamic equations of the heated panel subjected to an oscillating oblique shock are established by using Galerkin discrete method. Nonlinear vibration responses of the system are obtained by using the fourth-order Runge-Kutta numerical integration method to solve the nonlinear dynamic equations. It is found that vibration jump and bi-stable phenomena which are typical nonlinear dynamic behaviors exists. And then the effects of the strength of the incident shock wave, oscillating amplitude of the shock, temperature, location of the shock oscillation center and Mach number on the vibration jump and bi-stable phenomena of the system are studied. The results show that with the increase of the strength of the incident shock wave, oscillating amplitude of the shock and Mach number, the resonance peak values are increased monotonously, while the oscillating frequency interval for bi-stable state first widens from nonexistence, then narrows until it disappears, and then widens sharply; Increasing temperature will cause‘stiffness weakening effect’on the system; Moving the location of the shock oscillation center to both ends of the panel can effectively reduce the resonance peak values and suppress vibration jump behavior and bi-stable phenomena.

Key words： Oscillating shock waves primary resonance local piston theory vibration jump bi-site phenomenon nonlinear vibration

收稿日期: 2021-03-31 出版日期: 2022-05-15

引用本文:

叶柳青,叶正寅,洪正,叶坤. 振荡激波作用下受热壁板主共振特性分析[J]. 振动与冲击, 2022, 41(9): 41-50.
YE Liuqing, YE Zhengyin, HONG Zheng, YE Kun. Analysis of primary resonance characteristics of heated wall plate under oscillating shock wave. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(9): 41-50.

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http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I9/41

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