热声网络的辛对称特征

杨志春; 吴锋; 郭方中; 张春萍

doi:10.7498/aps.60.084303

摘要

将辛数学引入热声系统网络模型的处理,通过对热声系统网络传输矩阵的分析,证明系统中等温流体管道内工质运动的传输矩阵为辛矩阵.存在温度梯度的热声回热器中气体工质微团的传输矩阵不是辛矩阵,但是可以通过变量代换将传输矩阵转换为辛矩阵,使整个热声系统网络传输都可用辛矩阵传输来表示.辛对称的形式有助于热声系统网络模型的分析与计算.

关键词:

辛 /
热声 /
网络模型 /
传输矩阵

Symplectic mathematics is introduced into the thermoacoustic network model. The transferring matrix of thermoacoustic system is analyzed, and the transferring matrix of working gas in isothermal fluid pipe of thermoacoustic system is a symplectic matrix. The transferring matrix of working gas in regenerator of thermoacoustic system is not a symplectic matrix, but it can be converted into a symplectic matrix by variable transformation. With variable transformation, the whole transferring matrix of thermoacoustic system can be represented by a symplectic matrix. The form of symplectic matrix is conducible to analyzing and calculating the thermoacoutic network model.

Keywords:

作者及机构信息

1.
海军工程大学研究生院,武汉 430033;

2.
武汉工程大学理学院,武汉 430073;

3.
华中科技大学能源与动力工程学院,武汉 430074

基金项目: 国家自然科学基金(批准号:50676068)和湖北省教育厅科研计划重点项目(批准号:D200615002)资助的课题.

Authors and contacts

1.
Graduate School, Naval University of Engineering, Wuhan 430033, China;

2.
School of Science, Wuhan Institute of Technology, Wuhan 430073, China;

3.
School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

参考文献

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施引文献

[1]	Putnam A A 1956 J. Acoust. Soc. Am. 28 246
[2]
[3]	Rott N 1973 Z. Angew. Math. Phys. 24 54
[4]
[5]	Rott N 1975 Z. Angew. Math. Phys. 26 43
[6]	Ceperley P H 1979 J. Acoust. Soc. Am. 66 1508
[7]
[8]
[9]	Ceperley P H 1985 J. Acoust. Soc. Am. 77 1239
[10]
[11]	Swift G W 1988 J. Acoust. Soc. Am. 84 1145
[12]	Tominaga A 1995 Cryogenics 35 427
[13]
[14]
[15]	Xiao J H 1995 Cryogenics 35 15
[16]
[17]	Xiao J H 1995 Cryogenics 35 21
[18]
[19]	Xiao J H 1995 Cryogenics 35 27
[20]	Guo F Z 1985 On the Theory of Cyclic Flow Cryogenic Regenerator (Calcutta: International Conference on Cryogenics) p227
[21]
[22]	Guo F Z, Chou Y M, Lee S Z 1987 Cryogenics 27 152
[23]
[24]
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[26]
[27]	Deng X H, Hu X, Guo F Z 1996 Cryogenics 90 6 (in Chinese) [邓晓辉、胡晓、郭方中 1996低温工程 90 6]
[28]	Luo Z C 1988 Fluid Network Theory (Beijing: China Machine Press) p122 (in Chinese) [罗志昌 1988 流体网络理论 (北京: 机械工业出版社) 第122页]
[29]
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[31]	Swift G W 2001 Thermoacoustics: A Unifying Perpective for Some Engines and Refrigerators (New York: Acoustical Society of America) p90
[32]	Wu F, Guo F Z, Li D Y 2001 J. Appl. Sci. 19 362 (in Chinese) [吴锋、郭方中、李端勇 2001 应用科学学报 19 362]
[33]
[34]	Weyl H 1939 The Classical Groups,Their Invariants and Representations (Princeton: Princeton University Press) p1
[35]
[36]
[37]	Feng K,Qin M Z 2003 Symplectic Method in Hamilton System (Hangzhou: Zhejiang Science and Technology Press) p3 (in Chinese) [冯康、秦孟兆 2003 哈密顿系统的辛几何算法 (杭州: 浙江科学技术出版社) 第3页]
[38]
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[40]
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[47]
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[49]
[50]	Zhong W X 2003 Acta Mech. Sin. 35 401 (in Chinese)[钟万勰 2003 力学学报 35 401]
[51]
[52]
[53]	Yang H W, Zhong W X, Hou B H 2010 Acta Phys. Sin. 59 4437 (in Chinese) [杨红卫、钟万勰、侯碧辉 2010 59 4437]
[54]	Yang H W 2009 J.EEE 31 37 (in Chinese) [杨红卫 2009 电气电子教学学报 31 37]
[55]
[56]	Liang C H 2010 Saying Symmetry (Beijing: Science Press) p58 (in Chinese) [梁昌洪 2010 话说对称 (北京: 科学出版社) 第58页]
[57]
[58]
[59]	Hou G L,Alatancang 2008 Chin. Phys. B 17 2754
[60]
[61]	Cao Y, Yang K Q 2003 Acta Phys. Sin. 52 1984 (in Chinese) [曹禹、杨孔庆 2003 52 1984]
[62]
[63]	Luo X Y, Liu X S, Ding P Z 2007 Acta Phys. Sin. 56 604 (in Chinese) [罗香怡、刘学深、丁培柱 2007 56 604]
[64]
[65]	Zhang C L, Qi Y Y, Liu X S, Ding P Z 2009 Acta Phys. Sin. 58 3078 (in Chinese) [张春丽、祁月盈、刘学深、丁培柱 2009 58 3078]
[66]	Zhang C L, Qi Y Y, Liu X S, Ding P Z 2007 Acta Phys. Sin. 56 774 (in Chinese) [张春丽、祁月盈、刘学深、丁培柱 2007 56 774]
[67]
[68]
[69]	Wang H J 1991 Chin. J. Quantum Electron. 8 304 (in Chinese) [王洪吉 1991 量子电子学 8 304]
[70]
[71]	Wang H J 1993 J. Optoelectron. Laser 4 107 (in Chinese) [王洪吉 1993 光激光4 107]

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