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Steady loss factor is derived according to its definition, and a conclusion is obtained that steady loss factor is not always among modal loss factors but related to contributions of each modal response to vibration response. To obtain the conclusions about the range of steady loss factor, four cases are discussed according to positions of the two natural frequencies related to the central frequency. 1) Both natural frequencies are lower than the central frequency. 2) Both natural frequencies are higher than the central frequency. 3) One natural frequency, whose modal loss factor is smaller, is higher than the central frequency and the other natural frequency is lower than the central frequency. 4) One natural frequency, whose modal loss factor is larger, is higher than the central frequency and the other natural frequency is lower than the central frequency. Steady loss factor ranges between modal loss factors only if the frequency, whose value of multiplying modal loss factor is largest, is lower than central frequency of frequency band and at the same time, the frequency, whose value of multiplying modal loss factor is the smallest, is higher than the central frequency. Process loss factor which is a time-dependent function is proposed for the description of loss factor of decay process. Meanwhile, the way to calculate process loss factor with modal frequency, loss factor and amplitude is presented. Process loss factor tends to steady loss factor contributed by the mode with smallest loss factor over time. The accuracy is good enough for traditional decay rate method to estimate steady loss factor when there is only one mode or lots of modes in the frequency band. It is difficult for traditional decay rate method to be used to evaluate steady loss factor in the mid-frequency band where frequency density is not enough. A new method is proposed to estimate steady loss factor through separating the smallest modal loss factor components in the frequency band with time decay curve step by step according to the different decay characteristics. Simulation and experimental results indicate that the proposed method can cover the shortage of traditional decay rate method of estimating the steady loss factor in mid-frequency band.
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Keywords:
- steady loss factor /
- decay rate method /
- multimode frequency band
[1] Wang C, Zhou Y Q, Shen G W 2013 Chin. Phys. B 22 124601
[2] Li X G, Yang K D, Yang Y 2011 Chin. Phys. B 20 064302
[3] Pan X J, He X P 2010 Acta Phys. Sin. 59 7911(in Chinese) [潘晓娟, 贺西平 2010 59 7911]
[4] He X S, Deng F Y 2010 Acta Phys. Sin. 59 25(in Chinese) [和兴锁, 邓峰岩 2010 59 25]
[5] Lyon R H 1975 Statistical Energy Analysis of Dynamical Systems: Theory and Applications (MIT Press) pp3-10
[6] Fahy F J 1994 Philos. T. Roy. Soc. A 346 431
[7] Langley R S, Bardell N S 1998 Aeronaut. J. 102 287
[8] Zhang Q, Hao Z Y, Mao J, Chen X R 2014 Automot. Eng. 36 1004 (in Chinese) [张强, 郝志勇, 毛杰, 陈馨蕊 2014 汽车工程 36 1004]
[9] Yu M S, Zhu Z D 2007 J. Ship Mech. 11 273 (in Chinese) [俞孟萨, 朱正道 2007 船舶力学 11 273]
[10] Li X Z, Zhang X, Liu Q M, Zhang Z J, Li Y D 2013 J. China Railway Soc. 35 101 (in Chinese) [李小珍, 张迅, 刘全民, 张志俊, 李亚东 2013 铁道学报 35 101]
[11] Li L, Wen J H, Cai L 2013 Chin. Phys. B 22 014301
[12] Lei B, Yang K D, Ma Y L 2010 Chin. Phys. B 19 054301
[13] Ning F H, Zhang J 2002 J. Shangdong Inst. Technol. 16 17 (in Chinese) [宁方华, 张建 2002 山东工程学院学报 16 17]
[14] Cheng G L, Guan C B 2006 Noise and Vib. Control 26 105 (in Chinese) [程广利, 关成彬, 胡声亮 2006 噪声与振动控制 26 105]
[15] Schroeder R M 1965 J. Acou. Soc. Am 37 409
[16] Sheng M P, Wang M Q, Sun J C. 2001 J. Northwest. Polytechnical Univ. 19 130 (in Chinese) [盛美萍, 王敏庆, 孙进才 2001 西北工业大学学报 19 130]
[17] Yin B H, Wang M Q, Wu X D 2014 J. Vib. Shock 33 100 (in Chinese) [尹帮辉, 王敏庆, 吴晓东 2014 振动与冲击 33 100]
[18] Sheng M P 2001 Tech. Acoust. 20 56 (in Chinese) [盛美萍 2001 声学技术 20 56]
[19] Ungar E E, Edward J, Kerwin M 1962 J. Acoust. Soc. Am. 34 945
[20] Wang M Q, Sheng M P, Sun J C 2000 J. Northwest. Polytech. Univ. 18 553 (in Chinese) [王敏庆, 盛美萍, 孙进才 2000 西北工业大学学报 18 553]
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[1] Wang C, Zhou Y Q, Shen G W 2013 Chin. Phys. B 22 124601
[2] Li X G, Yang K D, Yang Y 2011 Chin. Phys. B 20 064302
[3] Pan X J, He X P 2010 Acta Phys. Sin. 59 7911(in Chinese) [潘晓娟, 贺西平 2010 59 7911]
[4] He X S, Deng F Y 2010 Acta Phys. Sin. 59 25(in Chinese) [和兴锁, 邓峰岩 2010 59 25]
[5] Lyon R H 1975 Statistical Energy Analysis of Dynamical Systems: Theory and Applications (MIT Press) pp3-10
[6] Fahy F J 1994 Philos. T. Roy. Soc. A 346 431
[7] Langley R S, Bardell N S 1998 Aeronaut. J. 102 287
[8] Zhang Q, Hao Z Y, Mao J, Chen X R 2014 Automot. Eng. 36 1004 (in Chinese) [张强, 郝志勇, 毛杰, 陈馨蕊 2014 汽车工程 36 1004]
[9] Yu M S, Zhu Z D 2007 J. Ship Mech. 11 273 (in Chinese) [俞孟萨, 朱正道 2007 船舶力学 11 273]
[10] Li X Z, Zhang X, Liu Q M, Zhang Z J, Li Y D 2013 J. China Railway Soc. 35 101 (in Chinese) [李小珍, 张迅, 刘全民, 张志俊, 李亚东 2013 铁道学报 35 101]
[11] Li L, Wen J H, Cai L 2013 Chin. Phys. B 22 014301
[12] Lei B, Yang K D, Ma Y L 2010 Chin. Phys. B 19 054301
[13] Ning F H, Zhang J 2002 J. Shangdong Inst. Technol. 16 17 (in Chinese) [宁方华, 张建 2002 山东工程学院学报 16 17]
[14] Cheng G L, Guan C B 2006 Noise and Vib. Control 26 105 (in Chinese) [程广利, 关成彬, 胡声亮 2006 噪声与振动控制 26 105]
[15] Schroeder R M 1965 J. Acou. Soc. Am 37 409
[16] Sheng M P, Wang M Q, Sun J C. 2001 J. Northwest. Polytechnical Univ. 19 130 (in Chinese) [盛美萍, 王敏庆, 孙进才 2001 西北工业大学学报 19 130]
[17] Yin B H, Wang M Q, Wu X D 2014 J. Vib. Shock 33 100 (in Chinese) [尹帮辉, 王敏庆, 吴晓东 2014 振动与冲击 33 100]
[18] Sheng M P 2001 Tech. Acoust. 20 56 (in Chinese) [盛美萍 2001 声学技术 20 56]
[19] Ungar E E, Edward J, Kerwin M 1962 J. Acoust. Soc. Am. 34 945
[20] Wang M Q, Sheng M P, Sun J C 2000 J. Northwest. Polytech. Univ. 18 553 (in Chinese) [王敏庆, 盛美萍, 孙进才 2000 西北工业大学学报 18 553]
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