[1] |
Iwatsubo T, Saigo M. Transverse vibration of a rotor system driven by a cardan joint. Journal of Sound and Vibration, 1984,95(1):9-18
|
[2] |
Doi M, Masuko I, Ito Y. et al. A study on parametric vibration in chuck work. Bulletin of JSME, 1985,28(245):2774-2780
|
[3] |
Warminski J, Litak G, Szabelski K. Synchronisation and chaos in a parametrically and self-excited system with two degrees of freedom. Nonlinear Dynamics, 2000,22(2):125-143
|
[4] |
Momeni M, Kourakis I, Moslehi-Fard M. et al. A van der Pol-Mathieu equation for the dynamics of dust grain charge in dusty plasmas, Journal of Physics A: Mathematical and Theoreitcal, 2007,40(24):F473-F481
|
[5] |
Belhaq M, Kirrou I, Mokni L. Periodic and quasiperiodic galloping of a wind-excited tower under external excitation. Nonlinear Dynamics, 2013,74(3):849-867
|
[6] |
Kirrou I, Mokni L, Belhaq M. On the quasiperiodic galloping of a wind-excited tower. Journal of Sound and Vibration, 2013,332(18):4059-4066
|
[7] |
Tondl A. On the interaction between self-excited and parametric vibrations. National Research Institute for Machine Design, Monographs and Memoranda No. 25, Prague 1978
|
[8] |
Kotera T, Yano S. Periodic solutions and the stability in a non-linear parametric excitation system. Bulletin of JSME, 1985,28(241):1473-1480
|
[9] |
陈予恕, 徐鉴. Van der pol-Duffing-Mathieu型系统主参数共振分岔解的普适分类. 中国科学A辑, 1995,25(12):1287-1297(Chen Yushu, Xu Jian. Van der Pol type-Duffing-Mathieu system primary parameter resonance bifurcation solution of the general classfication. Science in China A. 1995,25(12):1287-1297 (in Chinese))
|
[10] |
Szabelski K, Warminski J. Self-excited system vibrations with parametric and external excitation. Journal of Sound and Vibration, 1995,187(4):595-607
|
[11] |
彭献, 陈自力. 一类强非线性系统共振周期解的渐近分析. 动力学与控制, 2004,2(1):46-50(Peng Xian, Chen Zili. Asymptotic analysis for resonance cycle solution of a type of strongly nonlinear systems. Journal of Dynamics and Control. 2004,2(1):46-50 (in Chinese))
|
[12] |
Belhaq M, Fahsi A. 2:1 and 1:1 frequency-locking in fast excited van der Pol-Mathieu-Duffing oscillator. Nonlinear Dynamics, 2007,53(1-2):139-152
|
[13] |
Pandey M, Rand RH, Zehnder AT. Frequency locking in a forced Mathieu-van der Pol-Duffing system. Nonlinear Dynamics, 2007,54(1-2):3-12
|
[14] |
张琪昌, 冯晶晶, 王炜. 类Padé逼近方法在二维非线性振动系统的应用. 力学学报, 2011,43(5):914-921(Zhang Qichang, Feng Jingjing, Wang Wei. The construction of homoclinic and heteroclinic orbit in two-dimentsional nonlinear systems based on the quasi-Padé approximation, Chinese Journal of Theoretical and Applied Mechanics, 2011,43(5):914-921 (in Chinese))
|
[15] |
Warminski J. Nonlinear dynamics of self-, parametric, and externally excited oscillator with time delay: van der Pol versus Rayleigh models. Nonlinear Dynamics, 2019,99(1):35-56
|
[16] |
王延庆, 郭星辉, 梁宏琨 等. 凸肩叶片的非线性振动特性与运动分岔. 力学学报, 2011,43(4):755-764(Wang Yanqing, Guo Xinghui, Liang Hongkun, et al. Nonlinear vibratory characteristics and bifurcations of shrouded blades. Chinese Journal of Theoretical and Applied Mechanics. 2011,43(4):755-764 (in Chinese))
|
[17] |
张登博, 唐有绮, 陈立群. 非齐次边界条件下轴向运动梁的非线性振动. 力学学报, 2019,51(1):218-227(Zhang Dengbo, Tang Youqi, Chen Liqun. Nonlinear vibration of axially moving beams with nonhomogeneous boundary conditions. Chinese Journal of Theoretical and Applied Mechanics. 2019,51(1):218-227 (in Chinese))
|
[18] |
顾伟, 张博, 丁虎 等. 2:1 内共振条件下变转速预变形叶片的非线性动力学响应. 力学学报, 2020,52(4):1131-1142(Gu Wei, Zhang Bo, Ding Hu, et al. Nonlinear dynamic response of pre-deformation blade with variable rotational speed under 2:1 internal resonance. Chinese Journal of, Theoretical and Applied Mechanics, 2020,52(4):1131-1142 (in Chinese))
|
[19] |
陈娅昵, 孟文静, 钱有华 . 一类 Duffing 型系统的不动点混沌和 Fold/Fold 簇发现象及机理分析. 力学学报, 2020,52(5):1475-1484(Chen Yani, Meng Wenjing, Qian Youhua. Fixed point chaos and Fold/Fold bursting of a class of Duffing systems and the mechanism analysis. Chinese Journal of Theoretical and Applied Mechanics. 2020,52(5):1475-1484 (in Chinese))
|
[20] |
Nayfeh AH, Mook DT. Nonlinear Oscillations. Wiley, 1995
|
[21] |
Belhaq M, Houssni M. Quasi-periodic oscillations, chaos and suppression of chaos in a nonlinear oscillator driven by parametric and external excitations. Nonlinear Dynamics, 1999,18(1):1-24
|
[22] |
Abouhazim N, Belhaq M, Lakrad F. Three-period quasi-periodic solutions in the self-excited quasi-periodic Mathieu oscillator. Nonlinear Dynamics, 2005,39(4):395-409
|
[23] |
Fan Q, Leung AYT, Lee YY. Periodic and quasi-periodic responses of van der Pol-Mathieu system subject to various excitation. International Journal of Nonlinear Sciences and Numerical Simulation, 2016,17(1):29-40
|
[24] |
Veerman F, Verhulst F. Quasiperiodic phenomena in the van der Pol-Mathieu equation. Journal of Sound and Vibration, 2009,326(1-2):314-320
|
[25] |
Huang JL, Zhu WD. An incremental harmonic balance method with two timescales for quasiperiodic motion of nonlinear systems whose spectrum contains uniformly spaced sideband frequencies. Nonlinear Dynamics, 2017,90(2):1015-1033
|
[26] |
Huang JL, Zhu WD. A new incremental harmonic balance method with two time scales for quasi-periodic motions of an axially moving beam with internal resonance under single-tone external excitation. Journal of Vibration and Acoustics, 2017,139(2):021010
|
[27] |
Huang JL, Zhou WJ, Zhu WD. Quasi-periodic motions of high-dimensional nonlinear models of a translating beam with a stationary load subsystem under harmonic boundary excitation. Journal of Sound and Vibration, 2019,462:114870
|
[28] |
Cheung YK, Chen SH, Lau SL. Application of the incremental harmonic balance method to cubic non-linearity systems. Journal of Sound and Vibration, 1990,140(2):273-286
|
[29] |
陈树辉. 强非线性振动系统的定量分析方法. 北京: 科学出版社, 2007(Chen Shuhui. Quantitative Analysis Methods for Strongly Nonlinear Vibration. Beijing: Science Press, 2007 (in Chinese))
|
[30] |
Hsu CS. Impulsive parametric excitation: Theory. Journal of Applied Mechanics, 1972,39(2):551-558
|
[31] |
Hsu CS. On approximating a general linear periodic systems. Journal of Mathematical Analysis and Applications, 1974,45(1):234-251
|
[32] |
Hsu CS, Cheng WH. Applications of the theory of impulsive parametric excitation and new treatments of general parametric excitation problems. Journal of Applied Mechanics, 1973,40(1):78-86
|
[33] |
Friedmann P, Hammond CE, Woo TH. Efficient numerical treatment of periodic systems with application to stability problems. International Journal of Numerical Methods in Engineering, 1977,11(7):1117-1136
|
[34] |
Huang JL, Su RKL, Chen SH. Precise Hsu's method for analyzing the stability of periodic solutions of multi-degrees-of-freedom systems with cubic nonlinearity. Computers and Structures, 2009,87(23-24):1624-1630
|
[35] |
Zhong WX, Williams FW. A precise time step integration method. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 1994,208(6):427-430
|