Search

Article

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Vibrational resonance in a Duffing system with fractional-order external and intrinsic dampings driven by the two-frequency signals

Zhang Lu Xie Tian-Ting Luo Mao-Kang

Vibrational resonance in a Duffing system with fractional-order external and intrinsic dampings driven by the two-frequency signals

Zhang Lu, Xie Tian-Ting, Luo Mao-Kang
PDF
Get Citation

(PLEASE TRANSLATE TO ENGLISH

BY GOOGLE TRANSLATE IF NEEDED.)

  • The phenomenon of vibrational resonance (VR) in a Duffing system with both fractional-order external damping and fractional-order intrinsic damping driven by the two-frequency periodic signals is investigated. It is observed that the resonance amplitude Q can be optimized by an appropriate choice of the amplitude of the high-frequency signal. The obtained relationship between VR and the fractional-orders shows that both fractional-order external damping and fractional-order intrinsic damping can induce changes of the shapes of the effective potential function and then lead to more abundant resonance behaviors than in the traditional dynamic systems.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11171238), and the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (Grant No. 11221101).
    [1]

    Landa P S, McClintock P V E 2000 J. Phys. A: Math. Gen. 33 L433

    [2]

    Gitterman M 2005 Physica A 352 309

    [3]

    Lin M, Fang L M, Zhu R G 2008 Acta Phys. Sin. 57 2642 (in Chinese) [林敏, 方利民, 朱若谷 2008 物理学报 57 2642]

    [4]

    Baltans J P 2003 Phys. Rev. E 67 66119

    [5]

    Wang C J 2011 Chin. Phys. Lett. 28 090504

    [6]

    He Z Y, Zhou Y R 2011 Chin. Phys. Lett. 28 110505

    [7]

    Fang C J, Liu X B 2012 Chin. Phys. Lett. 29 050504

    [8]

    Yang J H, Liu X B 2010 J. Phys. A: Math. Theor. 43 122001

    [9]

    Guo F, Chen X F 2011 Journal of the Korean Physical Society 56 1567

    [10]

    Yang J H, Liu H G, Cheng G 2013 Acta Phys. Sin. 62 180503 (in Chinese) [杨建华, 刘后, 广程刚 2013 物理学报 62 180503]

    [11]

    Yang J H, Liu X.B. 2011 Phys. Scr. 83 065008

    [12]

    Hilfer R 2003 Applications of Fractional Calculus in Physics (Singapore: World Scientific)

    [13]

    Torvik P J, Bagley R L 1984 J. Appl. Mech. 51 294

    [14]

    Wang Z H, Hu H Y 2009 Science in China: G 39 1495 (in Chinese) [王在华, 胡海岩 2009 中国科学G辑 39 1495]

    [15]

    Tofighi A 2003 Physica A 329 29

    [16]

    Ryabov Y E, Puzenko A 2002 Phys. Rev. B 66 184201

    [17]

    Narahari Achar B N, Hanneken J W, Clarke T 2002 Physica A 309 275

    [18]

    Yang J H, Zhu H 2012 Chaos 22 13112

    [19]

    Petras I 2010 Fractional-order nonlinear system: modeling, analysis and simulation (Beijing: Higher Education Press)

  • [1]

    Landa P S, McClintock P V E 2000 J. Phys. A: Math. Gen. 33 L433

    [2]

    Gitterman M 2005 Physica A 352 309

    [3]

    Lin M, Fang L M, Zhu R G 2008 Acta Phys. Sin. 57 2642 (in Chinese) [林敏, 方利民, 朱若谷 2008 物理学报 57 2642]

    [4]

    Baltans J P 2003 Phys. Rev. E 67 66119

    [5]

    Wang C J 2011 Chin. Phys. Lett. 28 090504

    [6]

    He Z Y, Zhou Y R 2011 Chin. Phys. Lett. 28 110505

    [7]

    Fang C J, Liu X B 2012 Chin. Phys. Lett. 29 050504

    [8]

    Yang J H, Liu X B 2010 J. Phys. A: Math. Theor. 43 122001

    [9]

    Guo F, Chen X F 2011 Journal of the Korean Physical Society 56 1567

    [10]

    Yang J H, Liu H G, Cheng G 2013 Acta Phys. Sin. 62 180503 (in Chinese) [杨建华, 刘后, 广程刚 2013 物理学报 62 180503]

    [11]

    Yang J H, Liu X.B. 2011 Phys. Scr. 83 065008

    [12]

    Hilfer R 2003 Applications of Fractional Calculus in Physics (Singapore: World Scientific)

    [13]

    Torvik P J, Bagley R L 1984 J. Appl. Mech. 51 294

    [14]

    Wang Z H, Hu H Y 2009 Science in China: G 39 1495 (in Chinese) [王在华, 胡海岩 2009 中国科学G辑 39 1495]

    [15]

    Tofighi A 2003 Physica A 329 29

    [16]

    Ryabov Y E, Puzenko A 2002 Phys. Rev. B 66 184201

    [17]

    Narahari Achar B N, Hanneken J W, Clarke T 2002 Physica A 309 275

    [18]

    Yang J H, Zhu H 2012 Chaos 22 13112

    [19]

    Petras I 2010 Fractional-order nonlinear system: modeling, analysis and simulation (Beijing: Higher Education Press)

  • Citation:
Metrics
  • Abstract views:  1152
  • PDF Downloads:  574
  • Cited By: 0
Publishing process
  • Received Date:  30 August 2013
  • Accepted Date:  12 October 2013
  • Published Online:  05 January 2014

Vibrational resonance in a Duffing system with fractional-order external and intrinsic dampings driven by the two-frequency signals

  • 1. Department of Mathematics, Sichuan University, Chengdu 610065, China;
  • 2. Science and Technology on Electronic Information Control Laboratory, Chengdu 610036, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 11171238), and the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (Grant No. 11221101).

Abstract: The phenomenon of vibrational resonance (VR) in a Duffing system with both fractional-order external damping and fractional-order intrinsic damping driven by the two-frequency periodic signals is investigated. It is observed that the resonance amplitude Q can be optimized by an appropriate choice of the amplitude of the high-frequency signal. The obtained relationship between VR and the fractional-orders shows that both fractional-order external damping and fractional-order intrinsic damping can induce changes of the shapes of the effective potential function and then lead to more abundant resonance behaviors than in the traditional dynamic systems.

Reference (19)

Catalog

    /

    返回文章
    返回