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Shock and Vibration
Volume 18 (2011), Issue 1-2, Pages 257-268
http://dx.doi.org/10.3233/SAV-2010-0566

Asymptotical Behavior of the Solution of a SDOF Linear Fractionally Damped Vibration System

Z.H. Wang1,2 and M. L. Du1

1Institute of Science, PLA University of Science and Technology, 211101 Nanjing, China
2Institute of Vibration Engineering Research, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing, China

Received 3 February 2010; Revised 18 April 2010

Copyright © 2011 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [16 citations]

The following is the list of published articles that have cited the current article.

  • Yongjun Shen, Shaopu Yang, Haijun Xing, and Guosheng Gao, “Primary resonance of Duffing oscillator with fractional-order derivative,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 7, pp. 3092–3100, 2012. View at Publisher · View at Google Scholar
  • Yongjun Shen, Shaopu Yang, and Haijun Xing, “Super-harmonic resonance of fractional-order Duffing oscillator,” Lixue Xuebao/Chinese Journal of Theoretical and Applied Mechanics, vol. 44, no. 4, pp. 762–768, 2012. View at Publisher · View at Google Scholar
  • Yongjun Shen, Shaopu Yang, Haijun Xing, and Huaixiang Ma, “Primary resonance of Duffing oscillator with two kinds of fractional-order derivatives,” International Journal of Non-Linear Mechanics, vol. 47, no. 9, pp. 975–983, 2012. View at Publisher · View at Google Scholar
  • Yj Yu Ya-Juan, and Zh Wang Zai-Hua, “A Fractional-Order Phase-Locked Loop with Time-Delay and Its Hopf Bifurcation,” Chinese Physics Letters, vol. 30, no. 11, 2013. View at Publisher · View at Google Scholar
  • Zaihua Wang, and Haiyan Hu, “Stability and bifurcation of delayed dynamic systems: from theory to application,” Advances in Mechanics, vol. 43, no. 1, pp. 3–20, 2013. View at Publisher · View at Google Scholar
  • Yong-Jun Shen, Peng Wei, and Shao-Pu Yang, “Primary resonance of fractional-order van der Pol oscillator,” Nonlinear Dynamics, 2014. View at Publisher · View at Google Scholar
  • P Wei Peng, and Sp Yang Shao-Pu, “Super-harmonic resonance of fractional-order van der Pol oscillator,” Acta Physica Sinica, vol. 63, no. 1, 2014. View at Publisher · View at Google Scholar
  • Yongjun Shen, Peng Wei, Chuanyi Sui, and Shaopu Yang, “Subharmonic Resonance of Van Der Pol Oscillator with Fractional-Order Derivative,” Mathematical Problems in Engineering, 2014. View at Publisher · View at Google Scholar
  • Li-Li Liu, and Jun-Sheng Duan, “A detailed analysis for the fundamental solution of fractional vibration equation,” Open Mathematics, vol. 13, no. 1, 2015. View at Publisher · View at Google Scholar
  • Jun-Sheng Duan, Can Huang, and Li-Li Liu, “Response of a fractional nonlinear system to harmonic excitation by the averaging method,” Open Physics, vol. 13, no. 1, pp. 177–182, 2015. View at Publisher · View at Google Scholar
  • Qi Xu, Min Shi, and Zaihua Wang, “Stability and delay sensitivity of neutral fractional-delay systems,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 26, no. 8, pp. 084301, 2016. View at Publisher · View at Google Scholar
  • Shao-Fang Wen, Yong-Jun Shen, and Shao-Pu Yang, “Dynamical analysis of Duffing oscillator with fractional-order feedback with time delay,” Wuli Xuebao/Acta Physica Sinica, vol. 65, no. 9, 2016. View at Publisher · View at Google Scholar
  • Shaofang Wen, Yongjun Shen, Xianghong Li, and Shaopu Yang, “Dynamical analysis of Mathieu equation with two kinds of van der Pol fractional-order terms,” International Journal of Non-Linear Mechanics, 2016. View at Publisher · View at Google Scholar
  • Jingyu Hou, Xianghong Li, and Jufeng Chen, “Stability and slow-fast oscillation in fractional-order Belousov-Zhabotinsky reaction with two time scales,” Journal of Vibroengineering, vol. 18, no. 7, pp. 4812–4823, 2016. View at Publisher · View at Google Scholar
  • Jingfei Jiang, Dengqing Cao, Huatao Chen, and Kun Zhao, “The vibration transmissibility of a single degree of freedom oscillator with nonlinear fractional order damping,” International Journal of Systems Science, pp. 1–15, 2017. View at Publisher · View at Google Scholar
  • Shao-Fang Wen, Yong-Jun Shen, Shao-Pu Yang, and Jun Wang, “Dynamical response of Mathieu–Duffing oscillator with fractional-order delayed feedback,” Chaos, Solitons & Fractals, vol. 94, pp. 54–62, 2017. View at Publisher · View at Google Scholar