热梯度环境下梁高频振动的能量流模型

刘知辉; 牛军川; 贾睿昊

doi:10.7527/S1000-6893.2021.25336

航空学报 >

2022 , Vol. 43 >Issue 5: 425336 - 425336

DOI: https://doi.org/10.7527/S1000-6893.2021.25336

材料工程与机械制造

热梯度环境下梁高频振动的能量流模型

刘知辉 ,
牛军川 ,
贾睿昊

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1. 山东大学机械工程学院, 济南 250061;
2. 山东大学高效洁净机械制造教育部重点实验室, 济南 250061

收稿日期: 2021-01-28

修回日期: 2021-03-04

网络出版日期: 2021-05-10

基金资助

国家自然科学基金（51675306，52075294）；深圳市自然科学基金（JCYJ20190812170811682）

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Energy flow model for high-frequency vibration of beams in thermal-gradient environment

LIU Zhihui ,
NIU Junchuan ,
JIA Ruihao

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1. School of Mechanical Engineering, Shandong University, Jinan 250061, China;
2. Key Laboratory of High-Efficiency and Clean Mechanical Manufacture at Shandong University, Ministry of Education, Jinan 250061, China

Received date: 2021-01-28

Revised date: 2021-03-04

Online published: 2021-05-10

Supported by

National Natural Science Foundation of China (51675306, 52075294); Natural Science Foundation of Shenzhen (JCYJ20190812170811682)

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摘要

航空航天领域中的结构常由于高速飞行时的气动加热等因素在内外表面形成明显的温度差异，结构内部也常因此存在温度的梯度分布。为分析含有温度梯度的梁在高频激励下的动力学响应，建立了热梯度梁的能量流模型。首先通过求解热传导方程得到了梁内的温度场。然后考虑温度场对材料属性的影响，确定了梁的物理中性层以消除拉伸-弯曲变形耦合。基于哈密顿原理建立了梁的弯曲变形控制方程，进而得到了梁弯曲变形的波动频散关系。进一步推导得到了周期平均与局部空间平均后梁振动能量密度与能量流之间的关系，通过任意微元体内的能量平衡关系得到了热梯度环境下梁的能量流模型。与基准解的对比表明，建立的能量流模型能得到热梯度梁在高频激励下较为准确的振动能量分布情况。

关键词： 能量有限元; 能量流; 功率流有限元; 高频振动; 热环境

本文引用格式

刘知辉 , 牛军川 , 贾睿昊 . 热梯度环境下梁高频振动的能量流模型[J]. 航空学报, 2022 , 43(5) : 425336 -425336 . DOI: 10.7527/S1000-6893.2021.25336

Abstract

The structures in aerospace applications are usually exposed in extreme thermal environment due to the aerodynamic heating effect, thereby leading to the significant temperature difference between the internal and external surfaces of structures. As a result, the thermal gradient always exists inside the structures. To analyze the dynamic response of the beam exposed in thermal-gradient environment and subjected to high-frequency excitation, an energy flow model for the beams with thermal gradient is developed. The thermal field in the beam is solved by the thermal conduction equation. Considering the influences of the temperature on material properties, the physical neutral plane of the beam is determined to remove the stretch-bending coupling. The governing equations of deformation of the beam are derived using the Hamilton's principle to obtain the dispersion relation for the bending wave. Furthermore, the relationship between the energy density and energy intensity is deduced after the time-period average and local-space average. The governing equations for the energy density are attained by considering the power balance in any differential element. Compared with the benchmark solutions, the model proposed can give the accurate prediction of the vibrational energy density of the beam under the high-frequency excitation.

Key words： energy finite element method; power flow; power flow finite element method; high-frequency vibration; thermal environment

参考文献

[1] 杨雄伟, 李跃明, 耿谦. 基于混合FE-SEA法的高温环境飞行器宽频声振特性分析[J]. 航空学报, 2011, 32(10):1851-1859. YANG X W, LI Y M, GENG Q. Broadband vibro-acoustic response of aircraft in high temperature environment based on hybrid FE-SEA[J]. Acta Aeronautica et Astronautica Sinica, 2011, 32(10):1851-1859(in Chinese).
[2] 吴大方, 林鹭劲, 吴文军, 等. 1500℃极端高温环境下高超声速飞行器轻质隔热材料热/振联合试验[J]. 航空学报, 2020, 41(7):223612. WU D F, LIN L J, WU W J, et al. Thermal/vibration test of lightweight insulation material for hypersonic vehicle under extreme-high-temperature environment up to 1500℃[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(7):223612(in Chinese).
[3] 赵宏达, 丁继锋, 郝志伟, 等. 复杂航天器结构火工冲击环境预示方法研究[J]. 宇航学报, 2020, 41(1):35-43. ZHAO H D, DING J F, HAO Z W, et al. Study onprediction methods of pyroshock environment for complex spacecraft structures[J]. Journal of Astronautics, 2020, 41(1):35-43(in Chinese).
[4] CREMER L, HECKL M, PETERSSON B, et al. Structure-borne sound:structural vibrations and sound radiation at audio frequencies[J]. The Journal of the Acoustical Society of America, 2005, 118(5):2754.
[5] 王小东, 秦一凡, 季宏丽, 等. 基于声学黑洞效应的直升机驾驶舱宽带降噪[J]. 航空学报, 2020, 41(10):223831. WANG X D, QIN Y F, JI H L, et al. Broadband noise reduction inside helicopter cockpit with acoustic black hole effect[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(10):223831(in Chinese).
[6] 胡君逸, 李跃明, 李海波, 等. 考虑热应力、热变形正交各向异性板的动特性及响应规律[J]. 工程力学, 2018, 35(8):218-229. HU J Y, LI Y M, LI H B, et al. Researches on vibration characteristic and dynamic response of orthotropic plate with thermal stress and deformation[J]. Engineering Mechanics, 2018, 35(8):218-229(in Chinese).
[7] BANERJEE J R, SU H, JAYATUNGA C. A dynamic stiffness element for free vibration analysis of composite beams and its application to aircraft wings[J]. Computers & Structures, 2008, 86(6):573-579.
[8] CHEN Z L, YANG Z C, GU Y S, et al. An energy flow model for high-frequency vibration analysis of two-dimensional panels in supersonic airflow[J]. Applied Mathematical Modelling, 2019, 76:495-512.
[9] KAYA M O. Free vibration analysis of a rotating Timoshenko beam by differential transform method[J]. Aircraft Engineering and Aerospace Technology, 2006, 78(3):194-203.
[10] GU L L, QIN Z Y, CHU F L. Analytical analysis of the thermal effect on vibrations of a damped Timoshenko beam[J]. Mechanical Systems and Signal Processing, 2015, 60-61:619-643.
[11] AVSEC J, OBLAK M. Thermal vibrational analysis for simply supported beam and clamped beam[J]. Journal of Sound and Vibration, 2007, 308(3-5):514-525.
[12] CHEN Q, MA W Y, FEI Q G, et al. An efficient wave based method for the mid-frequency transverse vibration analysis of a thermal beam with interval uncertainties[J]. Aerospace Science and Technology, 2021, 110:106438.
[13] LANGLEY R S, CORDIOLI J A. Hybrid deterministic-statistical analysis of vibro-acoustic systems with domain couplings on statistical components[J]. Journal of Sound and Vibration, 2009, 321(3-5):893-912.
[14] LE BOT A. Foundation of statistical energy analysis in vibroacoustics[M]. Oxford:Oxford University Press, 2015.
[15] 陈强, 张鹏, 李彦斌, 等. 热环境下长宽比对L型折板统计能量分析参数的影响研究[J]. 振动与冲击, 2018, 37(4):191-196, 202. CHEN Q, ZHANG P, LI Y B, et al. Effect of aspect ratio on statistical energy analysis parameters of L-shaped folded plate under thermal environment[J]. Journal of Vibration and Shock, 2018, 37(4):191-196, 202(in Chinese).
[16] 陈强, 张鹏, 李彦斌, 等. 基于FEM-PIM计及热效应的统计能量分析[J]. 航空动力学报, 2017, 32(6):1366-1374. CHEN Q, ZHANG P, LI Y B, et al. Statistical energy analysis considering thermal effect based on FEM-PIM[J]. Journal of Aerospace Power, 2017, 32(6):1366-1374(in Chinese).
[17] CHEN Q, FEI Q G, LI Y B, et al. Prediction of statistical energy analysis parameters in thermal environment[J]. Journal of Spacecraft and Rockets, 2019, 56(3):687-694.
[18] 胡婉璐, 陈海波, 钟强. 轴力对梁结构耦合损耗因子的影响研究[J]. 振动与冲击, 2020, 39(17):24-30. HU W L, CHEN H B, ZHONG Q. Effects of axial force on coupling loss factor of beam structures[J]. Journal of Vibration and Shock, 2020, 39(17):24-30(in Chinese).
[19] 代文强, 郑旭, 郝志勇, 等. 采用能量有限元分析的高速列车车内噪声预测[J]. 浙江大学学报(工学版), 2019, 53(12):2396-2403. DAI W Q, ZHENG X, HAO Z Y, et al. Prediction of high-speed train interior noise using energy finite element analysis[J]. Journal of Zhejiang University (Engineering Science), 2019, 53(12):2396-2403(in Chinese).
[20] 王怀志, 于开平, 张宗强, 等. 仪器舱结构的能量有限元中频声振环境预示[J]. 振动与冲击, 2019, 38(10):143-148. WANG H Z, YU K P, ZHANG Z Q, et al. Prediction of the acoustic-vibration environment of an instrument cabin by using the energy finite element method[J]. Journal of Vibration and Shock, 2019, 38(10):143-148(in Chinese).
[21] 陈兆林, 杨智春, 王用岩, 等. 基于能量有限元法和虚拟模态综合法的高频冲击响应分析方法[J]. 航空学报, 2018, 39(8):221893. CHEN Z L, YANG Z C, WANG Y Y, et al. A high-frequency shock response analysis method based on energy finite element method and virtual mode synthesis and simulation[J]. Acta Aeronautica et Astronautica Sinica, 2018, 39(8):221893(in Chinese).
[22] 滕晓艳, 丰国宝, 江旭东, 等. 自由阻尼梁高频能量流响应的解析模型[J]. 航空学报, 2019, 40(4):222616. TENG X Y, FENG G B, JIANG X D, et al. Analytical model of high-frequency energy flow response for a beam with free layer damping[J]. Acta Aeronautica et AstronauticaSinica, 2019, 40(4):222616(in Chinese).
[23] ZHANG W B, CHEN H L, ZHU D H, et al. The thermal effects on high-frequency vibration of beams using energy flow analysis[J]. Journal of Sound and Vibration, 2014, 333(9):2588-2600.
[24] WANG D, XIE M X, LI Y M. High-frequency dynamic analysis of plates in thermal environments based on energy finite element method[J]. Shock and Vibration, 2015, 2015:157208.
[25] WANG X C, YANG Z C, WANG W, et al. Nonlinear viscoelastic heated panel flutter with aerodynamic loading exerted on both surfaces[J]. Journal of Sound and Vibration, 2017, 409:306-317.
[26] DOWELL E H. Nonlinear oscillations of a fluttering plate[J]. AIAA Journal, 1966, 4(7):1267-1275.
[27] SHE G L, YUAN F G, REN Y R. Thermal buckling and post-buckling analysis of functionally graded beams based on a general higher-order shear deformation theory[J]. Applied Mathematical Modelling, 2017, 47:340-357.
[28] RAO S S. Vibration of continuous systems[M]. Hoboken:John Wiley & Sons, Inc., 2006.
[29] NAVAZI H M, NOKHBATOLFOGHAHAEI A, GHOBAD Y, et al. Experimental measurement of energy density in a vibrating plate and comparison with energy finite element analysis[J]. Journal of Sound and Vibration, 2016, 375:289-307.
[30] WOHLEVER J C, BERNHARD R J. Mechanical energy flow models of rods and beams[J]. Journal of Sound and Vibration, 1992, 153(1):1-19.
[31] CHEN Z L, YANG Z C, GUO N, et al. An energy finite element method for high frequency vibration analysis of beams with axial force[J]. Applied Mathematical Modelling, 2018, 61:521-539.

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