Forced vibration of a fractional-order single degree-of-freedom oscillator with clearance

被引：0
作者：
Niu J. [1 ,2 ]
Zhao Z. [2 ]
Xing H. [1 ,2 ]
Shen Y. [1 ,2 ]
机构：
[1] State Key Laboratory of Mechanical Behavior in Traffic Engineering Structure and System Safety, Shijiazhuang Tiedao University, Shijiazhuang
[2] School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang
来源：
Zhendong yu Chongji/Journal of Vibration and Shock | 2020年 / 39卷 / 14期
关键词：
Approximate analytical solution; Fractional-order derivative; Krylov-Bogoliubov-Mitropoisky (KBM) asymptotic method; Primary resonance;
D O I：
10.13465/j.cnki.jvs.2020.14.034
中图分类号：
学科分类号：
摘要：
The forced vibration of a single degree-of-freedom piecewise linear oscillator with a clearance and a fractional-order derivative term was investigated. The approximate analytical solution for its primary resonance was obtained by the Krylov-Bogoliubov-Mitropoisky (KBM) asymptotic method. The primary resonance of the piecewise linear system was analyzed, and a unified expression of the fractional-order differential term was obtained, where the fractional order was restricted in 0 to 2. The effects of the fractional-order differential term on the dynamic characteristics of the piecewise system were expressed as an equivalent linear damping and an equivalent linear stiffness, while that of the clearance was an equivalent nonlinear stiffness. The expression of the amplitude-frequency response of the primary resonance was obtained, and the stability condition of the system was also achieved. The approximate analytical solutions and numerical solutions of the primary resonance amplitude-frequency responses were compared, which shows both are in good agreement. The effects of the fractional-order term and clearance on the amplitude-frequency response of the primary resonance were analyzed in detail. It concludes that the KBM asymptotic method is an effective method to analyze the dynamics of fractional-order piecewise smooth systems. © 2020, Editorial Office of Journal of Vibration and Shock. All right reserved.
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页码：251 / 256and284
相关论文
共 31 条
  • [21] JIA J H, SHEN X Y, HUA H X., Viscoelastic behavior analysis and application of the fractional derivative maxwell model, Journal of Vibration and Control, 13, 13, pp. 385-401, (2007)
  • [22] SHOKOOH A, SUAREZ L., A comparison of numerical methods applied to a fractional model of damping materials, Journal of Vibration and Control, 5, 3, pp. 331-354, (1999)
  • [23] DROZDOV A D., Fractional differential models in finite viscoelasticity, Acta Mechanica, 124, 1, pp. 155-180, (1997)
  • [24] SHEN Y J, WEI P, YANG S P., Primary resonance of fractional-order Van der Pol oscillator, Nonlinear Dynamics, 77, 4, pp. 1629-1642, (2014)
  • [25] SHEN Y J, NIU J C, YANG S P, Et al., Primary resonance of dry-friction oscillator with fractional-order proportional-integral-derivative controller of velocity feedback, Journal of Computational and Nonlinear Dynamics, 11, 5, (2016)
  • [26] YANG T Z., Stability in parametric resonance of an axially moving beam constituted by fractional order material, Archive of Applied Mechanics, 82, 12, pp. 1763-1770, (2012)
  • [27] YANG Jianhua, ZHU Hua, The response property of one kind of factional-order linear system excited by different periodical signals, Acta Physica Sinica, 62, 2, (2013)
  • [28] XU Y, LI Y G, LIU D., A method to stochastic dynamical systems with strong nonlinearity and fractional damping, Nonlinear Dynamics, 83, 4, pp. 2311-2321, (2016)
  • [29] SHEN Yongjun, YANG Shaopu, XING Haijun, Dynamical analysis of linear single degree-of-freedom oscillator with fractional-order derivative, Acta Physica Sinica, 61, 11, (2012)
  • [30] (2007)
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