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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.
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Keywords:
- vibrational resonance /
- Duffing system /
- fractional-order damping /
- fractional system
[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)
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[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)
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