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Symplectic symmetry feature of thermoacoustic network

Yang Zhi-Chun Wu Feng Guo Fang-Zhong Zhang Chun-Ping

Symplectic symmetry feature of thermoacoustic network

Yang Zhi-Chun, Wu Feng, Guo Fang-Zhong, Zhang Chun-Ping
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  • 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.
    • Funds:
    [1]

    Putnam A A 1956 J. Acoust. Soc. Am. 28 246

    [2]
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    Rott N 1973 Z. Angew. Math. Phys. 24 54

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    Rott N 1975 Z. Angew. Math. Phys. 26 43

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    Ceperley P H 1979 J. Acoust. Soc. Am. 66 1508

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    Ceperley P H 1985 J. Acoust. Soc. Am. 77 1239

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    Tominaga A 1995 Cryogenics 35 427

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    Xiao J H 1995 Cryogenics 35 15

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    Xiao J H 1995 Cryogenics 35 21

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    Xiao J H 1995 Cryogenics 35 27

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    Guo F Z 1985 On the Theory of Cyclic Flow Cryogenic Regenerator (Calcutta: International Conference on Cryogenics) p227

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    Guo F Z, Chou Y M, Lee S Z 1987 Cryogenics 27 152

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    Guo F Z, Li Q 2007 Heat Dynamics (Wuhan: Huazhong University of Science and Technology Press) p165 (in Chinese) [郭方中、李 青 2007 热动力学 (武汉: 华中科技大学出版社) 第165页]

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    Swift G W 2001 Thermoacoustics: A Unifying Perpective for Some Engines and Refrigerators (New York: Acoustical Society of America) p90

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    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]

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    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]

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    Zhong W X 2002 Dual System in Applied Mechanics (Beijing: Science Press) p28 (in Chinese) [钟万勰 2002 应用力学对偶体系 (北京: 科学出版社) 第28页]

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    Zhong W X 2010 Force, Work, Energy and Symplectic Mathematics (Dalian: Dalian University of Technology Press) p1 (in Chinese) [钟万勰 2010 力、功、能量与辛数学 (大连: 大连理工大学出版社) 第1页]

    [42]

    Zhong W X 2006 Symplectic Solution Methodology in Applied Mechanics (Beijing: Higher Education Press) p12 (in Chinese) [钟万勰 2006 应用力学的辛数学方法 (北京: 高等教育出版社) 第12页 ]

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    Zhong W X 1993 J. Dalian Univ. Techn. 33 110 (in Chinese) [钟万勰 1993 大连理工大学学报 33 110]

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    [46]

    Zhong W X 2001 J. Dalian Univ. Techn. 41 379 (in Chinese) [钟万勰 2001 大连理工大学学报 41 379]

    [47]
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    Chen J F,Zhu B,Zhong W X 2009 Acta Phys. Sin. 58 1091 (in Chinese)[陈杰夫、朱 宝、钟万勰 2009 物理学报 58 1091]

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    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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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]

  • [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]
    [25]

    Guo F Z, Li Q 2007 Heat Dynamics (Wuhan: Huazhong University of Science and Technology Press) p165 (in Chinese) [郭方中、李 青 2007 热动力学 (武汉: 华中科技大学出版社) 第165页]

    [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]
    [30]
    [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]
    [39]

    Zhong W X 2002 Dual System in Applied Mechanics (Beijing: Science Press) p28 (in Chinese) [钟万勰 2002 应用力学对偶体系 (北京: 科学出版社) 第28页]

    [40]
    [41]

    Zhong W X 2010 Force, Work, Energy and Symplectic Mathematics (Dalian: Dalian University of Technology Press) p1 (in Chinese) [钟万勰 2010 力、功、能量与辛数学 (大连: 大连理工大学出版社) 第1页]

    [42]

    Zhong W X 2006 Symplectic Solution Methodology in Applied Mechanics (Beijing: Higher Education Press) p12 (in Chinese) [钟万勰 2006 应用力学的辛数学方法 (北京: 高等教育出版社) 第12页 ]

    [43]
    [44]

    Zhong W X 1993 J. Dalian Univ. Techn. 33 110 (in Chinese) [钟万勰 1993 大连理工大学学报 33 110]

    [45]
    [46]

    Zhong W X 2001 J. Dalian Univ. Techn. 41 379 (in Chinese) [钟万勰 2001 大连理工大学学报 41 379]

    [47]
    [48]

    Chen J F,Zhu B,Zhong W X 2009 Acta Phys. Sin. 58 1091 (in Chinese)[陈杰夫、朱 宝、钟万勰 2009 物理学报 58 1091]

    [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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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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Publishing process
  • Received Date:  27 September 2010
  • Accepted Date:  15 March 2011
  • Published Online:  05 April 2011

Symplectic symmetry feature of thermoacoustic network

  • 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

Abstract: 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.

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