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Low frequency band gaps and vibration reduction properties of a multi-frequency locally resonant phononic plate

Wu Jian Bai Xiao-Chun Xiao Yong Geng Ming-Xin Yu Dian-Long Wen Ji-Hong

Low frequency band gaps and vibration reduction properties of a multi-frequency locally resonant phononic plate

Wu Jian, Bai Xiao-Chun, Xiao Yong, Geng Ming-Xin, Yu Dian-Long, Wen Ji-Hong
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  • A multi-frequency locally resonant (LR) phononic plate is proposed in this paper. The phononic plate consists of periodic arrays of multiple double-cantilevered thin beams attached to a thin homogeneous plate. This proposed phononic plate is simplified and modeled using a plane wave expansion method to enable the calculation of flexural wave band structures. The band gap behavior of the phononic plate is analyzed comprehensively. In addition, an experimental specimen is fabricated using a square aluminum plate with a thickness of 0.9 mm and an area of 840 mm840 mm, and attached to the specimens as periodic arrays of two types of double-cantilevered thin beams made of the same material as the host plate. And the specimen is measured by using a scanning laser Doppler vibrometer to verify the theoretical predictions of band gaps. Investigations of this paper yield the following findings and conclusions: (1) Due to the interaction of low-frequency vibrational modes of attached multiple double-cantilevered beams and flexural vibration of the host plate, the proposed multi-frequency LR phononic plate can exhibit multiple low-frequency flexural wave band gaps (stop bands). It is also found that the band gaps of a multi-frequency LR phononic plate, especially those appearing in a lower frequency range, are generally narrower than that of a single-frequency LR phononic plate with the same type of double-cantilevered beams. (2) The frequency location of band gaps moves to higher frequency range when the thickness of the double-cantilevered beams is increased, or when the length of the double-cantilevered beams is decreased. It is also shown that a very small variation of the thickness (e. g., 0.1 mm) may lead to significant changes of frequency position of the band gaps. (3) When the width of the double-cantilevered beams is enlarged or the number of the double-cantilevered beams is increased, the lower band gap edge will move to a lower frequency range, while the upper band gap edge will move to a higher frequency range. This implies that the bandwidth of the band gaps is broadened. However, at the same time, it is shown that the central frequencies of the band gaps remain almost unchanged. (4) Experimental measurements of the fabricated specimen evidence the existence of two low frequency band gaps, and confirm that the flexural plate vibrations are significantly reduced in the predicted band gaps.
      Corresponding author: Xiao Yong, xiaoy@vip.sina.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51305448), the Aeronautical Science Fund, Chinia (Grant No. 2015ZA88003), and the Science and Technology Project of State Grid Company of China (Grant No. 5299001352UC).
    [1]

    Kushwaha M S, Halevi P, Dobrzynski L, Djafari-Rouhani B 1993 Phys. Rev. Lett. 71 2022

    [2]

    Liu Z, Zhang X, Mao Y, Zhu Y Y, Yang Z, Chan C T, Sheng P 2000 Science 289 1734

    [3]

    Fang N, Xi D, Xu J, Ambati M, Strituravanich W, Sun C, Zhang X 2006 Nat. Mater. 5 452

    [4]

    Wen X S, Wen J H, Yu D L, Wang G, Liu Y Z, Han X Y 2009 Phononic Crystals (Beiging: National Defense Industry Press) pp196-291 (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196-291页]

    [5]

    Wen J H, Wang G, Yu D L, Zhao H G, Liu Y Z, Wen X S 2008 Sci. China Series E: Technol. Sci. 51 85

    [6]

    Cheng C, Wu F G, Zhang X, Yao Y W 2014 Acta Phys. Sin. 63 024301 (in Chinese) [程聪, 吴福根, 张欣, 姚源卫 2014 物理学报 63 024301]

    [7]

    Liu J, Hou Z L, Fu X J 2015 Acta Phys. Sin. 64 154302 (in Chinese) [刘娇, 侯志林, 傅秀军 2015 物理学报 64 154302]

    [8]

    Zhang H, Wen J H, Chen S B, Wang G, Wen X S 2015 Chin. Phys. B 24 036201

    [9]

    Xiao Y, Wen J, Wen X 2012 Phys Lett A 376 1384

    [10]

    Xiao Y, Wen J, Yu D, Wen X 2013 J. Sound Vib. 332 867

    [11]

    Xiao Y, Wen J, Wang G, Wen X 2013 J. Vib. Acoust. 135 041006

    [12]

    Wang Y F, Wang Y S 2013 J. Sound Vib. 332 2019

    [13]

    Xiao Y, Wen J, Wen X 2012 New J. Phys. 14 033042

    [14]

    Zhang H, Wen J, Xiao Y, Wang G, Wen X 2015 J. Sound Vib. 343 104

    [15]

    Zhang H, Xiao Y, Wen J, Yu D, Wen X 2015 J. Phys. D: Appl. Phys. 48 435305

    [16]

    Zhang Y, Wen J, Xiao Y, Wen X, Wang J 2012 Phys Lett A 376 1489

    [17]

    Liu Z, Chan C T, Sheng P 2005 Phys. Rev. B 71 014103

    [18]

    Li J, Chan C T 2004 Phys. Rev. E 70 055602(R)

    [19]

    Yu D L, Liu Y Z, Qiu J, Zhao H G, Liu Z M 2005 Chin. Phys. Lett. 22 1958

    [20]

    Wu T T, Huang Z G, Tsai T C, Wu T C 2008 Appl. Phys. Lett. 93 111902

    [21]

    Pennec Y, Djafari-Rouhani B, Larabi H, Vasseur J O, Hladky-Hennion A C 2008 Phys. Rev. B 78 104105

    [22]

    Oudich M, Assouar M B, Hou Z 2010 Appl. Phys. Lett. 97 193503

    [23]

    Oudich M, Senesi M, Assouar M B, Ruzenne M, Sun J H, Vincent B, Hou Z, Wu T T 2011 Phys. Rev. B 84 165136

    [24]

    Xiao Y, Wen J, Wen X 2012 J. Sound Vib. 331 5408

    [25]

    Xiao Y, Wen J, Wen X 2012 J. Phys. D: Appl. Phys. 45 195401

    [26]

    Zhang S, Wu J H, Hu Z 2013 J. Appl. Phys. 113 163511

    [27]

    Wang Y F, Wang Y S 2013 J. Appl. Phys. 114 043509

    [28]

    Ma J, Hou Z, Assouar B M 2014 J. Appl. Phys. 115 093508

    [29]

    Xiao Y, Wen J, Huang L, Wen X 2014 J. Phys. D: Appl. Phys. 47 045307

    [30]

    Torrent D, Mayou D, Snchez-Dehesa J 2013 Phys. Rev. B 87 115143

  • [1]

    Kushwaha M S, Halevi P, Dobrzynski L, Djafari-Rouhani B 1993 Phys. Rev. Lett. 71 2022

    [2]

    Liu Z, Zhang X, Mao Y, Zhu Y Y, Yang Z, Chan C T, Sheng P 2000 Science 289 1734

    [3]

    Fang N, Xi D, Xu J, Ambati M, Strituravanich W, Sun C, Zhang X 2006 Nat. Mater. 5 452

    [4]

    Wen X S, Wen J H, Yu D L, Wang G, Liu Y Z, Han X Y 2009 Phononic Crystals (Beiging: National Defense Industry Press) pp196-291 (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196-291页]

    [5]

    Wen J H, Wang G, Yu D L, Zhao H G, Liu Y Z, Wen X S 2008 Sci. China Series E: Technol. Sci. 51 85

    [6]

    Cheng C, Wu F G, Zhang X, Yao Y W 2014 Acta Phys. Sin. 63 024301 (in Chinese) [程聪, 吴福根, 张欣, 姚源卫 2014 物理学报 63 024301]

    [7]

    Liu J, Hou Z L, Fu X J 2015 Acta Phys. Sin. 64 154302 (in Chinese) [刘娇, 侯志林, 傅秀军 2015 物理学报 64 154302]

    [8]

    Zhang H, Wen J H, Chen S B, Wang G, Wen X S 2015 Chin. Phys. B 24 036201

    [9]

    Xiao Y, Wen J, Wen X 2012 Phys Lett A 376 1384

    [10]

    Xiao Y, Wen J, Yu D, Wen X 2013 J. Sound Vib. 332 867

    [11]

    Xiao Y, Wen J, Wang G, Wen X 2013 J. Vib. Acoust. 135 041006

    [12]

    Wang Y F, Wang Y S 2013 J. Sound Vib. 332 2019

    [13]

    Xiao Y, Wen J, Wen X 2012 New J. Phys. 14 033042

    [14]

    Zhang H, Wen J, Xiao Y, Wang G, Wen X 2015 J. Sound Vib. 343 104

    [15]

    Zhang H, Xiao Y, Wen J, Yu D, Wen X 2015 J. Phys. D: Appl. Phys. 48 435305

    [16]

    Zhang Y, Wen J, Xiao Y, Wen X, Wang J 2012 Phys Lett A 376 1489

    [17]

    Liu Z, Chan C T, Sheng P 2005 Phys. Rev. B 71 014103

    [18]

    Li J, Chan C T 2004 Phys. Rev. E 70 055602(R)

    [19]

    Yu D L, Liu Y Z, Qiu J, Zhao H G, Liu Z M 2005 Chin. Phys. Lett. 22 1958

    [20]

    Wu T T, Huang Z G, Tsai T C, Wu T C 2008 Appl. Phys. Lett. 93 111902

    [21]

    Pennec Y, Djafari-Rouhani B, Larabi H, Vasseur J O, Hladky-Hennion A C 2008 Phys. Rev. B 78 104105

    [22]

    Oudich M, Assouar M B, Hou Z 2010 Appl. Phys. Lett. 97 193503

    [23]

    Oudich M, Senesi M, Assouar M B, Ruzenne M, Sun J H, Vincent B, Hou Z, Wu T T 2011 Phys. Rev. B 84 165136

    [24]

    Xiao Y, Wen J, Wen X 2012 J. Sound Vib. 331 5408

    [25]

    Xiao Y, Wen J, Wen X 2012 J. Phys. D: Appl. Phys. 45 195401

    [26]

    Zhang S, Wu J H, Hu Z 2013 J. Appl. Phys. 113 163511

    [27]

    Wang Y F, Wang Y S 2013 J. Appl. Phys. 114 043509

    [28]

    Ma J, Hou Z, Assouar B M 2014 J. Appl. Phys. 115 093508

    [29]

    Xiao Y, Wen J, Huang L, Wen X 2014 J. Phys. D: Appl. Phys. 47 045307

    [30]

    Torrent D, Mayou D, Snchez-Dehesa J 2013 Phys. Rev. B 87 115143

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  • Received Date:  07 August 2015
  • Accepted Date:  12 November 2015
  • Published Online:  20 March 2016

Low frequency band gaps and vibration reduction properties of a multi-frequency locally resonant phononic plate

    Corresponding author: Xiao Yong, xiaoy@vip.sina.com
  • 1. State Grid Shaanxi Electric Power Research Institute, Xi'an 710054, China;
  • 2. Laboratory of Science and Technology on Integrated Logistics Support, and College of Mechatronic Engineering and Automation, National University of Defense Technology, Changsha 410073, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 51305448), the Aeronautical Science Fund, Chinia (Grant No. 2015ZA88003), and the Science and Technology Project of State Grid Company of China (Grant No. 5299001352UC).

Abstract: A multi-frequency locally resonant (LR) phononic plate is proposed in this paper. The phononic plate consists of periodic arrays of multiple double-cantilevered thin beams attached to a thin homogeneous plate. This proposed phononic plate is simplified and modeled using a plane wave expansion method to enable the calculation of flexural wave band structures. The band gap behavior of the phononic plate is analyzed comprehensively. In addition, an experimental specimen is fabricated using a square aluminum plate with a thickness of 0.9 mm and an area of 840 mm840 mm, and attached to the specimens as periodic arrays of two types of double-cantilevered thin beams made of the same material as the host plate. And the specimen is measured by using a scanning laser Doppler vibrometer to verify the theoretical predictions of band gaps. Investigations of this paper yield the following findings and conclusions: (1) Due to the interaction of low-frequency vibrational modes of attached multiple double-cantilevered beams and flexural vibration of the host plate, the proposed multi-frequency LR phononic plate can exhibit multiple low-frequency flexural wave band gaps (stop bands). It is also found that the band gaps of a multi-frequency LR phononic plate, especially those appearing in a lower frequency range, are generally narrower than that of a single-frequency LR phononic plate with the same type of double-cantilevered beams. (2) The frequency location of band gaps moves to higher frequency range when the thickness of the double-cantilevered beams is increased, or when the length of the double-cantilevered beams is decreased. It is also shown that a very small variation of the thickness (e. g., 0.1 mm) may lead to significant changes of frequency position of the band gaps. (3) When the width of the double-cantilevered beams is enlarged or the number of the double-cantilevered beams is increased, the lower band gap edge will move to a lower frequency range, while the upper band gap edge will move to a higher frequency range. This implies that the bandwidth of the band gaps is broadened. However, at the same time, it is shown that the central frequencies of the band gaps remain almost unchanged. (4) Experimental measurements of the fabricated specimen evidence the existence of two low frequency band gaps, and confirm that the flexural plate vibrations are significantly reduced in the predicted band gaps.

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