EI、Scopus 收录
中文核心期刊

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

含时滞反馈与涨落质量的记忆阻尼系统的随机共振

公徐路 许鹏飞

公徐路, 许鹏飞. 含时滞反馈与涨落质量的记忆阻尼系统的随机共振[J]. 力学学报, 2018, 50(4): 880-889. doi: 10.6052/0459-1879-18-051
引用本文: 公徐路, 许鹏飞. 含时滞反馈与涨落质量的记忆阻尼系统的随机共振[J]. 力学学报, 2018, 50(4): 880-889. doi: 10.6052/0459-1879-18-051
Gong Xulu, Xu Pengfei. STOCHASTIC RESONANCE OF A MEMORIAL-DAMPED SYSTEM WITH TIME DELAY FEEDBACK AND FLUCTUATING MASS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(4): 880-889. doi: 10.6052/0459-1879-18-051
Citation: Gong Xulu, Xu Pengfei. STOCHASTIC RESONANCE OF A MEMORIAL-DAMPED SYSTEM WITH TIME DELAY FEEDBACK AND FLUCTUATING MASS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(4): 880-889. doi: 10.6052/0459-1879-18-051

含时滞反馈与涨落质量的记忆阻尼系统的随机共振

doi: 10.6052/0459-1879-18-051
基金项目: 山西省回国留学人员科研资助项目(2015-068).
详细信息
    作者简介:

    *公徐路, 助教, 主要研究方向: 随机动力系统. E-mail:xulgong@163.com

    通讯作者:

    公徐路

  • 中图分类号: O324;

STOCHASTIC RESONANCE OF A MEMORIAL-DAMPED SYSTEM WITH TIME DELAY FEEDBACK AND FLUCTUATING MASS

  • 摘要: 针对具有记忆效应的欠阻尼系统, 存在时滞反馈与涨落质量, 本文主要研究了其输出稳态响应振幅的随机共振效应. 首先通过引入新变量和运用小时滞近似展开理论, 将具有非马尔科夫特性的原系统转化为等价的两维马尔科夫线性系统, 再利用Shapiro-Loginov公式和Laplace变换获得了系统响应的一阶稳态矩和稳态响应振幅的解析表达式. 结果表明: 当系统参数满足Routh-Hurwitz稳定条件时, 稳态响应振幅随质量涨落噪声强度、周期驱动信号频率以及时滞的变化均存在随机共振现象, 其中随机多共振现象也被观察到. 在适当范围内, 通过控制时滞反馈, 系统的随机共振效应随着时滞的增大而增强, 而较长的记忆时间及增大阻尼参数均对共振行为呈现抑制作用.有效调控时滞反馈与记忆效应的变化关系将有助于增强系统对周期驱动信号的响应强度. 最后, 通过数值模拟计算验证了理论结果的有效性.

     

  • [1] Benzi R, Sutera A, Vulpiani A.The mechanism of stochastic resonance.Journal of Physics A: Mathematical and General, 1981,14(11): L453-L457
    [2] Gammaitoni L, Hänggi P, Jung P, et al.Stochastic Resonance.Reviews of Modern Physics, 1998, 70(1): 223-287
    [3] Jin YF, Ma ZM, Xiao SM.Coherence and stochastic resonance in a periodic potential driven by multiplicative dichotomous and additive white noise.Chaos Solitons & Fractals, 2017, 103: 470-475
    [4] Gitterman M, Shapiro I.Stochastic resonance in a harmonic oscillator with random mass subject to asymmetric dichotomous noise.Journal of Statistical Physics, 2011, 144(1): 139-149
    [5] Wu J, Xu Y, Wang HY.Information-based measures for logical stochastic resonance in a synthetic gene network under Lévy flight superdiffusion.Chaos, 2017, 27(6): 339-342
    [6] Nicolis C, Nicolis G.Stochastic resonance across bifurcation cascades.Physical Review E, 2017, 95(3): 032219-8
    [7] Kang YM, Wang M, Xie Y.Stochastic resonance in coupled weakly-damped bistable oscillators subjected to additive and multiplicative noises.Acta Mechanica Sinica, 2012, 28(2): 505-510
    [8] Zheng RC, Nakano K, Hu HG, et al.An application of stochastic resonance for energy harvesting in a bistable vibrating system.Journal of Sound & Vibration, 2014, 333(12): 2568-2587
    [9] Berdichevsky V, Gitterman M.Stochastic resonance in linear systems subject to multiplicative and additive noise.Physical Review E, 1999, 60(2): 1494-1499
    [10] Li JM, Chen XF, He Z.Multi-stable stochastic resonance and its application research on mechanical fault diagnosis.Journal of Sound & Vibration, 2013, 332(22): 5999-6015
    [11] Siegle P, Goychuk I, Hänggi P.Origin of hyperdiffusion in generalized Brownian motion.Physical Review Letters, 2010, 105(10): 100602-4
    [12] Wang KG, Tokuyama M.Nonequilibrium statistical description of anomalous diffusion.Physica A, 1996, 265(3): 341-351
    [13] Plyukhin AV.Nonergodic solutions of the generalized Langevin equation.Physical Review E, 2011, 83(6): 062102-3
    [14] Bao JD, Bai ZW.Ballistic diffusion of a charged particle in a blackbody radiation field.Chinese Physics Letters, 2005, 22(8): 1845-1847
    [15] Bao JD.Numerical integration of a non-markovian langevin equation with a thermal band-passing noise.Journal of Statistical Physics, 2004, 114(1-2): 503-513
    [16] Bao JD, Zhuo YZ.Ballistic diffusion induced by a thermal broadband noise.Physical Review Letters, 2003, 91(13): 138104-4
    [17] 谢文贤, 许鹏飞, 蔡力等. 随机双指数记忆耗散系统的非马尔可夫扩散. 物理学报, 2013, 62(8): 080503-6
    [17] (Xie Wenxian, Xu Pengfei, Cai Li, et al.Non-markovian diffusion of the stochastic system with a biexponentical dissipative memory kernel.Acta Physica Sinica, 2013, 62(8), 080503-6 (in Chinese))
    [18] Srokowski T.Bistable generalised langevin dynamics driven by correlated noise possessing a long jump distribution: Barrier crossing and stochastic resonance.European Physical Journal B, 2013, 86(5): 239-245
    [19] Neiman A, Sung W.Memory effects on stochastic resonance.Physics Letters A, 1996, 223(5): 341-347
    [20] Kim S, Park SH, Pyo HB.Stochastic resonance in coupled oscillator systems with time delay.Physical Review Letters, 1999, 82(8): 1620-1623
    [21] 胡海岩, 赵永辉, 黄锐. 飞机结构气动弹性分析与控制研究. 力学学报, 2016, 48(1): 1-27
    [21] (Hu Haiyan, Zhao Yonghui, Huang Rui.Studies on aeroelastic analysis and control of aircraft structures.Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(1): 1-27 (in Chinese))
    [22] Morse R, Longtin A.Coherence and stochastic resonance in threshold crossing detectors with delayed feedback.Physics Letters A, 2006, 359(6): 640-646
    [23] 申永军, 赵永香, 田佳雨等. 一类含时滞的半主动悬架系统的动力学分析. 力学学报, 2013, 45(5): 755-762
    [23] (Shen Yongjun, Zhao Yongxiang, Tian Jiayu, et al.Dynamical analysis on a kind of semi-active suspension with time delay.Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(5): 755-762 (in Chinese))
    [24] Sun ZK, Yang XL, Xiao YZ.Modulating resonance behaviors by noise recycling in bistable systems with time delay.Chaos, 2014, 24(2): 023126-6
    [25] 张舒, 徐鉴. 时滞耦合系统非线性动力学的研究进展. 力学学报, 2017, 49(3): 565-587
    [25] (Zhang Shu, Xu Jian.Review on nonlinear dynamics in systems with coulpling delays.Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(3): 565-587 (in Chinese))
    [26] Jin YF.Noise-induced dynamics in a delayed bistable system with correlated noises.Physica A, 2012, 391(5): 1928-1933
    [27] Zhong SC, Zhang L, Wang HQ, et al.Nonlinear effect of time delay on the generalized stochastic resonance in a fractional oscillator with multiplicative polynomial noise.Nonlinear Dynamics, 2017, 89(2): 1324-1340
    [28] Yu HT, Wang J, Du JW, et al.Effects of time delay on the stochastic resonance in small-world neuronal networks.Chaos, 2013, 23(1): 013128-7
    [29] Gitterman M.Harmonic oscillator with fluctuating damping parameter.Physical Review E, 2004, 69(4): 041101-4
    [30] 谢文贤, 李东平, 许鹏飞等. 具有固有频率涨落的记忆阻尼线性系统的随机共振. 物理学报, 2014, 63(10): 100502-8
    [30] (Xie Wenxian, Li Dongping, Xu Pengfei, et al.Stochastic resonance of a memorial-damped linear system with natural frequency fluctuation.Acta Physica Sinica, 2014, 63(10): 100502-8 (in Chinese))
    [31] Gitterman M.Oscillator with random trichotomous mass.Physica A, 2012, 391(22): 5343-5348
    [32] Rubì JM, Gadomski A.Nonequilibrium thermodynamics versus model grain growth: derivation and some physical implications.Physica A, 2003, 326(3): 333-343
    [33] Pérez AT, Saville D, Soria C.Modeling the electrophoretic deposition of colloidal particles.Europhysics Letters, 2001, 55(3): 425-431
    [34] Guillouzic S, L’Heureux I, Longtin A. Small delay approximation of stochastic delay differential equations.Physical Review E, 1999, 59(4): 3970-3982
    [35] Shapiro VE, Loginov VM.“Formulae of differentiation” and their use for solving stochastic equations.Physica A, 1978, 91(3): 563-574
    [36] 刘秉正, 彭建华. 非线性动力学. 北京: 高等教育出版社, 2004
    [36] (Liu Bingzheng, Peng Jianhua. Nonlinear Dynamics.Beijing: Higher Education Press, 2004 (in Chinese))
    [37] Gammaitoni L, Marchesoni F, Santucci S.Stochastic resonance as a bona fide resonance.Physical Review Letters, 1995, 74(7): 1052-1055
  • 加载中
计量
  • 文章访问数:  1611
  • HTML全文浏览量:  102
  • PDF下载量:  264
  • 被引次数: 0
出版历程
  • 刊出日期:  2018-07-18

目录

    /

    返回文章
    返回