振荡激波作用下受热壁板主共振特性分析

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (9) : 41-50.

论文

振荡激波作用下受热壁板主共振特性分析

叶柳青,叶正寅,洪正,叶坤

作者信息 +

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

YE Liuqing, YE Zhengyin, HONG Zheng, YE Kun

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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。

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.

导出引用

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[J]. Journal of Vibration and Shock, 2022, 41(9): 41-50

参考文献

[1] 丁一波，岳晓奎，代洪华，等. 考虑进气约束的高超声速飞行器预定性能控制[J]. 航空学报，2021, 42：X24838.
DING Yibo, YUE Xiaokui, DAI Honghua, et al. Prescribed performance controller for flexible air-breathing hypersonic vehicle with inlet unstart constraint [J]. Acta Aeronautica et Astronautica Sinica, 2021, 42：X24838.
[2] DING Y B, WANG X G, BAI Y L, et al. Global smooth sliding mode controller for flexible air-breathing hypersonic vehicle with actuator faults [J]. Aerospace Science and Technology, 2019, 92: 563-578.
[3] CHENG Z A, CHEN F Y, GONG J X. Self-repairing control of air-breathing hypersonic vehicle with actuator fault and backlash [J]. Aerospace Science and Technology, 2020, 97: 105608.
[4] URZAY J. Supersonic combustion in air-breathing propulsion systems for hypersonic flight [J]. Annual Review of Fluid Mechanics, 2018, 50: 593-627.
[5] PETHA S. VIGNESH R, TAE H K, et al. Effects of back pressure perturbation on shock strain oscillations in a rectangular duct [J]. Acta Astronautica, 2021, 179: 525-535.
[6] YU J, AMIN P, SEYED M M, et al. Effect of cavity back height on mixing efficiency of hydrogen multi-jets at supersonic combustion chamber [J]. International Journal of Hydrogen Energy, 2020, 45(51): 27828-27836.
[7] 徐以勒，俞凯凯，徐惊雷. 几何尺寸约束的超燃冲压发动机推力喷管研究[J]. 航空学报，2021,42（4）:124259.
CHEN Yile, YU Kaikai, XU Jinglei. A new design method on scramjet nozzles with strong geometric constraints [J]. Acta Aeronautica et Astronautica Sinica, 2020, 42(4): 124259.
[8] 叶柳青，叶正寅. 激波主导流动下壁板的热气动弹性稳定性理论分析[J]. 力学学报, 2018, 50(2): 221-232.
Ye Liuqing, Ye Zhengyin. Aeroelastic stability analysis of heated flexible panel in shock-dominated flows [J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(2): 221-232.
[9] 叶正寅，孟宪宗，刘成, 等. 高超声速飞行器气动弹性的近期进展与发展展望[J]. 空气动力学学报, 2018, 36(6):984-997.
YE Zhengyin, MENG Xianzong, LIU Cheng, et al. Progess and prospects on aeroelasticity of hypersonic vehicles[J]. Acta Aerodynamica Sinica, 2018, 36(6):984-997.
[10] 李映坤，陈雄，许进升. 基于流固耦合的斜激波冲击作用下曲壁板气动弹性分析[J]. 航空动力学学报, 2020, 35(4): 783-792 Li Yinkun, Chen Xiong, Xu Jinsheng. Aeroelastic analysis of curved panels subjected to impinging oblique shock based on fluid-structure coupling algorithm [J]. Journal of Aerospace Power, 2020, 35(4): 783-792.
[11] MILLER B, CROWELL A， MCNAMARA J J. Modeling and
analysis of shock impingements on thermo-mechanically compliant surface panels[C]// 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference.Honolulu:AIAA, 2012.
[12] VISBAL M R. On the interaction of an oblique shock with a flexible panel [J]. Journal of Fluids and Structures, 2012, 30: 219-225.
[13] VISBAL M R. Viscous and inviscid interactions of an oblique shock with a flexible panel [J]. Journal of Fluids and Structures, 2014, 48: 27-45.
[14] BOYER N R, MCNAMARA J J, GAITONDE D V, et al. Features of panel flutter response to shock boundary layer interactions [J]. Journal of Fluids and Structures, 2021, 101: 1-27.
[15] BROUWER K R, CROWELL A R, MCNAMARA J J. Rapid prediction of unsteady aeroelastic loads in shock-dominated flows. 56th AIAA/ASCE/AHS/ASC Structures , Structural Dynamics, and Materials Conference, 2015
[16] YE L Q, YE Z Y, WANG X C. Aeroelastic stability analysis of heated flexible panel subjected to an oblique shock [J]. Chinese Journal of Aeronautics, 2018, 31(8):1650-1666.
[17] YE L Q, YE Z Y. Effects of shock location on aeroelastic stability of flexible panel [J]. AIAA Journal, 2018, 56(9): 3732-3744.
[18] DENNIS D, SEBASTIAN W, ALI G. Experiments on the interaction of a fast-moving shock with an elastic panel [J]. AIAA Journal, 2016, 54(2): 670-678.
[19] OKAJIMA M, BURROUGHS C B, CHARPIE J P. An analytic model for the frequencies of resonance of rectangular plates of variable curvature and thickness[J]. The Journal of the Acoustical Society of America, 1995, 97(2): 1053-1060.
[20] DU G J, LIU X M, HU Y D, et al. Nonlinear superharmonic resonance of damped circular sandwich plates with initial deflection[J]. Advanced Materials Research, 2011, 199/200: 1080-1083.
[21] XUE C X, REN X J. Nonlinear principal resonance of magneto-electro-elastic thin plate[J]. Journal of Measurement Science & Instrumentation, 2014, 5(4): 93-98.
[22] 张小广，胡宇达，任兴利. 四边固支功能梯度矩形板的主共振分析[J].振动与冲击, 2011, 30(6): 153-157.
ZHANG Xiaoguang, HU Yuda, REN Xingli. Nonlinear principle resonance of clamped functionally graded rectangular plate[J]. Journal of Vibration and Shock, 2011, 30(6): 153-157.
[23] HU Y D, WANG T. Nonlinear resonance of the rotating circular plate under static loads in magnetic field[J]. Chinese Journal of Mechanical Engineering, 2015, 28(6): 1277-1284.
[24] 马冰冰，胡宇达. 横向常磁场中铁磁圆板的主共振特性与静载效应[J]. 振动与冲击，2021,40(1): 308-316.
MA Bingbing, HU Yuda. Principal resonance characteristics and static load effect of a ferromagnetic circular plate in a transverse constant magnetic field[J]. Journal of Vibration and Shock, 2021, 40(1): 308-316.
[25] WANG X Z, HUANG X Y. A simple modeling and experiment on dynamic stability of a disk rotating in air[J]. Journal of Structural Stability and Dynamics, 2008, 8(1): 41-60.
[26] 李文强，胡宇达. 气动载荷下旋转运动圆板磁弹性主共振分析[J]. 力学季刊, 2018, 39(2): 339-349.
LI Wenqiang, HU Yuda. Magneto-elastic primary resonance of a rotating conductive circular plate under aerodynamic load[J]. Chinese Quarterly of Mechanics, 2018, 39(2): 339-349.
[27] 贺理浩, 张启帆, 岳连捷, 等. 高速进气道低马赫数不起动特性及马赫数影响规律[J]. 推进技术, 2021, 1-11
HE Lihao, ZHANG Qifan, YUE Lianjie, et al. Unstart characteristics of high speed inlet at low Mach number and influence law of Mach number [J]. Journal of Propulsion Technology, 2021, 1-11.
[28] 黄蓉，李祝飞，聂宝平, 等. 带抽吸气二元进气道/隔离段激波串振荡特性[J]. 推进技术, 2020, 41(4): 767-777.
HUANG Rong, LI Zhufei, NIE Baoping, et al. Shock train oascillations in a two-dimensional inlet/isolator with suction[J]. Journal of Propulsion Technology, 2020, 41(4): 767-777.
[29] 徐珂靖，常军涛，李楠, 等. 背景波系下的隔离段激波串运动特性及其流动机理研究[J]. 实验流体力学, 2019, 33(3): 31-42
XU Kejing, CHANG Juntao, LI Nan, et al. Recent research progress on motion characteristics and flowmechanism of shock train in an isolator with background waves[J]. Journal of Experiments in Fluid Mechanics, 2019, 33(3): 31-42.
[30] 周建，杨智春，谷迎松. 两面受气动载荷的壁板热弹性稳定性分析[J]. 中国科学：技术科学，2012, 42(12): 1416-1422.
ZHOU Jian, YANG Zhichun, GU Yingsong. Aeroelastic stability analysis of heated panel with aerodynamic loading on both surface[J]. Scientia sinica Technologica, 2012, 42(12): 1416-1422.
[31] 叶献辉，杨翊仁，范晨光. 热环境下壁板非线性颤振分析[J]. 计算力学学报, 2009, 26(5): 684-689.
YE Xianhui, YANG Yiren, FAN Chenguang. Nonlinear flutter analysis of a panel in the thermal environment [J]. Chinese Journal of Computational Mechanics, 2009, 26(5): 684-689.
[32] 陈大林，吴连军，钟卫洲. 考虑气动力非线性时二维受热壁板的颤振分析[J].工程力学, 2011， 28(12): 226-230.
Chen Dalin, Wu Lianjun, Zhong Weizhou. Flutter analysis of a two-dimensional heated panel considering nonlinear aerodynamics[J]. Engineering Mechanics, 2011 28(12): 226-230.
[33] 杨智春，夏巍. 壁板颤振的分析模型、数值求解方法和研究进展 [J]. 力学进展, 2010, 40(1): 81-98.
YANG Zhichun, XIA Wei. Analytical models, numerical solutions and advances in the study of panel flutter[J]. Advances in Mechanics, 2010, 40(1): 81-98.
[34] Lighthill M J. Oscillating airfoils at high mach number[J]. Journal of Aeornautical Science, 1953, 20(6): 402-406.
[35] Ashely H, Zartarian G. Piston theory — a new aerodynamic tool for aeroelastician[J]. Journal of Aeornautical Science, 1956, 23(10): 1109-1118.
[36] DOWELL E H. Nonlinear oscillations of a fluttering plate[J]. AIAA Journal, 1966, 4(7): 1267-1275.
[37] DAI H, YUE X, YUAN J, et al. A comparison of classical Runge-Kutta and Heonon’s methods for capturaring chaos and chaotic transients in an aeroelastic system with freeplay nonlineaity[J]. Nonlinear Dynamics, 2015, 81(1-2): 169-188.
[38] YE L Q, YE Z Y. Theoretical analysis for the effect of static pressure differential on aeroelastic stability of flexible panel[J]. Aerospace Science and Technology, 2021, 109: 1-18.