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Statistical energy analysis (SEA) is widely used in predicting dynamic response of complex coupled systems. This paper studies the bending wave propagation in periodic rib-stiffened plates in the framework of SEA. Effect of frequency band gap property of the rib-stiffened plate and wave filtering characteristics of the stiffened ribs on the prediction results of SEA is analyzed by using the wave approach and Bloch theory. It is found that due to the fact that classic SEA ignores an energy “tunneling mechanism” between subsystems that are not physically connected, large error up to almost 40 dB is generated in the subsystems of the plate compared with the results calculated from the finite element method. This tunneling mechanism mainly results from the wave filtering effects caused by the periodic arrangement of the ribs and it plays a significant role on the subsystem response at high frequencies. However, this is not incorporated in the modelling of classic SEA thus large errors can occur. To solve this problem, an advanced statistical energy analysis (ASEA) is used to consider the transition, transmission and transport of energy between unconnected subsystems. ASEA divides the energy of each subsystem into two parts: available energy which is the modal energy that could transmit into connected subsystems, and unavailable energy that dissipates within the subsystem; therefore the energy cannot propagate further away. Then the ray tracing algorithm is used to track the power flow across subsystems. By using ASEA, the accuracy of the prediction results can be greatly improved so that the error is reduced to less than 5 dB in most frequency bands. An experimental set-up is also designed to support the plate by simulating the simply-supported boundary conditions along the edges. The test results agree well with the finite element method, and it is sufficient to validate the theoretical models.
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Keywords:
- rib-stiffened plate /
- statistical energy analysis /
- periodic structures /
- tunneling mechanism
[1] Lu T J, Xin F X 2012 Fundamentals of vibration and acoustics for structural design of lightweight plates and shells (Beijing: Science Press) p1 (in Chinese) [卢天健, 辛锋先 2012 轻质板壳结构设计的振动和声学基础 (北京: 科学出版社) 第 1 页]
[2] Fahy F, Gardonio P 2007 Sound and Structural Vibration: Radiation, Transmission and Response 2nd Ed. (Oxford: Academic Press)
[3] Yin J, Yin J F, Hopkins C 2015 J. Sound Vib. 344 221
[4] Wen J H, Yu D L, Wang G 2007 Acta Phys. Sin. 56 2298 (in Chinese) [温激鸿, 郁殿龙, 王刚 2007 物理学报 56 2298]
[5] Xiao Y, Wen J H, Wen X S 2012 J. Phys. D: Appl. Phys. 45 195401
[6] Xiao Y, Wen J H, Huang L 2014 J. Phys. D: Appl. Phys. 47 045307
[7] Mead D J 1996 J. Sound Vib. 190 495
[8] Golub M V, Fomenko S I, Bui T Q 2012 Int. J. Solids Struct. 49 344
[9] Ji L, Joki C M, Huang Z 2013 Trans. FAMENA 37 29
[10] Brunskog J, Chung H 2011 J. Acoust. Soc. Am. 129 1336
[11] Zhao Z M, Sheng M P, Yang Y 2013 Eng. Mech. 30 239 (in Chinese) [赵芝梅, 盛美萍, 杨阳 2013 工程力学 30 239]
[12] Remillieux M C, Burdisso R A 2012 J. Acoust. Soc. Am. 132 36
[13] Li S, Zhao D Y 2001 Acta Acoust. 26 174 (in Chinese) [黎胜, 赵德有 2001 声学学报 26 174]
[14] Lyon R H, Dejong R G 1995 Theory and application of Statistical Energy Analysis (2nd Ed.) (Newton: Butterworth-Heinemann)
[15] Langley R S, Smith J R, Fahy F J 1997 J. Sound Vib. 208 407
[16] Blakemore M, Woodhouse J, Hardie D 1999 J. Sound Vib. 222 813
[17] Blakemore M, Woodhouse J 1998 IUTAM Symposium on Statistical Energy Analysis (London: Kluwer Academic Publishers) p163
[18] Langley R S 1989 J. Sound Vib. 135 499
[19] Langley R S, Bercin A N 1994 Phil. Trans. B 346 489
[20] Sheng M P 2002 Eng. Sci. 6 77 (in Chinese) [盛美萍 2002 中国工程科学 6 77]
[21] Heron K H 1994 Phil. Trans. A 346 501
[22] Langley R S 1992 J. Sound Vib. 159 483
[23] Sun J C 1995 Acta Acoust. 2 127 (in Chinese) [孙进才 1995 声学学报 2 127]
[24] Lalor N 1990 ISVR Report No. 190 (University of Southampton)
[25] Yin J F, Hopkins C 2013 J. Acoust. Soc. Am. 4 2069
[26] Cremer L, Heckl M, Ungar E E 1988 Structure-Borne Sound (2nd Ed.) (Berlin: Springer-Verlag)
[27] Tso Y K, Hansen C H 1998 J. Sound Vib. 215 63
[28] Wen X S, Wen J H, Yu D L, Wang G, Liu Y Z, Han X Y 2009 Phononic crystals (Beijing: National Defense Industry Press) p34 (in Chinese) [温熙森, 温激鸿, 郁殿龙, 王刚, 刘耀宗, 韩小云 2009 声子晶体 (北京: 国防工业出版社) 第34页]
[29] Hopkins C 2007 Sound insulation (Oxford: Butter- worth-Heinemann) p580
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[1] Lu T J, Xin F X 2012 Fundamentals of vibration and acoustics for structural design of lightweight plates and shells (Beijing: Science Press) p1 (in Chinese) [卢天健, 辛锋先 2012 轻质板壳结构设计的振动和声学基础 (北京: 科学出版社) 第 1 页]
[2] Fahy F, Gardonio P 2007 Sound and Structural Vibration: Radiation, Transmission and Response 2nd Ed. (Oxford: Academic Press)
[3] Yin J, Yin J F, Hopkins C 2015 J. Sound Vib. 344 221
[4] Wen J H, Yu D L, Wang G 2007 Acta Phys. Sin. 56 2298 (in Chinese) [温激鸿, 郁殿龙, 王刚 2007 物理学报 56 2298]
[5] Xiao Y, Wen J H, Wen X S 2012 J. Phys. D: Appl. Phys. 45 195401
[6] Xiao Y, Wen J H, Huang L 2014 J. Phys. D: Appl. Phys. 47 045307
[7] Mead D J 1996 J. Sound Vib. 190 495
[8] Golub M V, Fomenko S I, Bui T Q 2012 Int. J. Solids Struct. 49 344
[9] Ji L, Joki C M, Huang Z 2013 Trans. FAMENA 37 29
[10] Brunskog J, Chung H 2011 J. Acoust. Soc. Am. 129 1336
[11] Zhao Z M, Sheng M P, Yang Y 2013 Eng. Mech. 30 239 (in Chinese) [赵芝梅, 盛美萍, 杨阳 2013 工程力学 30 239]
[12] Remillieux M C, Burdisso R A 2012 J. Acoust. Soc. Am. 132 36
[13] Li S, Zhao D Y 2001 Acta Acoust. 26 174 (in Chinese) [黎胜, 赵德有 2001 声学学报 26 174]
[14] Lyon R H, Dejong R G 1995 Theory and application of Statistical Energy Analysis (2nd Ed.) (Newton: Butterworth-Heinemann)
[15] Langley R S, Smith J R, Fahy F J 1997 J. Sound Vib. 208 407
[16] Blakemore M, Woodhouse J, Hardie D 1999 J. Sound Vib. 222 813
[17] Blakemore M, Woodhouse J 1998 IUTAM Symposium on Statistical Energy Analysis (London: Kluwer Academic Publishers) p163
[18] Langley R S 1989 J. Sound Vib. 135 499
[19] Langley R S, Bercin A N 1994 Phil. Trans. B 346 489
[20] Sheng M P 2002 Eng. Sci. 6 77 (in Chinese) [盛美萍 2002 中国工程科学 6 77]
[21] Heron K H 1994 Phil. Trans. A 346 501
[22] Langley R S 1992 J. Sound Vib. 159 483
[23] Sun J C 1995 Acta Acoust. 2 127 (in Chinese) [孙进才 1995 声学学报 2 127]
[24] Lalor N 1990 ISVR Report No. 190 (University of Southampton)
[25] Yin J F, Hopkins C 2013 J. Acoust. Soc. Am. 4 2069
[26] Cremer L, Heckl M, Ungar E E 1988 Structure-Borne Sound (2nd Ed.) (Berlin: Springer-Verlag)
[27] Tso Y K, Hansen C H 1998 J. Sound Vib. 215 63
[28] Wen X S, Wen J H, Yu D L, Wang G, Liu Y Z, Han X Y 2009 Phononic crystals (Beijing: National Defense Industry Press) p34 (in Chinese) [温熙森, 温激鸿, 郁殿龙, 王刚, 刘耀宗, 韩小云 2009 声子晶体 (北京: 国防工业出版社) 第34页]
[29] Hopkins C 2007 Sound insulation (Oxford: Butter- worth-Heinemann) p580
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