ON THE HOMOCLINIC ORBITS IN A CLASS OF TWO-DEGREE-OF-FREEDOM SYSTEMS UNDER THE RESONANCE CONDITIONS

Applied Mathematics and Mechanics (English Edition) ›› 2001, Vol. 22 ›› Issue (3): 340-352.

ON THE HOMOCLINIC ORBITS IN A CLASS OF TWO-DEGREE-OF-FREEDOM SYSTEMS UNDER THE RESONANCE CONDITIONS

王茂南, 徐振源

Mathematics and Physics Institute, Wuxi University of Light Industry, Wuxi 214036, P. R. China

收稿日期:2000-05-08 修回日期:2000-10-29 出版日期:2001-03-18 发布日期:2001-03-18
基金资助:
the National Natural Science Foundation of China(19872044)

ON THE HOMOCLINIC ORBITS IN A CLASS OF TWO-DEGREE-OF-FREEDOM SYSTEMS UNDER THE RESONANCE CONDITIONS

WANG Mao-nan, XU Zhen-yuan

Mathematics and Physics Institute, Wuxi University of Light Industry, Wuxi 214036, P. R. China

Received:2000-05-08 Revised:2000-10-29 Online:2001-03-18 Published:2001-03-18
Supported by:
the National Natural Science Foundation of China(19872044)

摘要/Abstract

摘要： A class of two-degree-of-freedom systems in resonance with an external, parametric excitation is investigated, the existence of the periodic solutions locked to Ω is proved by the use of the method of multiple scales. This systems can be transformed into the systems of Wiggins under some conditions. A calculating formula which determines the existence of homoclinic orbits of the systems is given.

关键词: a two-degree-of-freedom system, method of multiple scales, periodic solution, homoclinic orbit, chaos

Abstract: A class of two-degree-of-freedom systems in resonance with an external, parametric excitation is investigated, the existence of the periodic solutions locked to Ω is proved by the use of the method of multiple scales. This systems can be transformed into the systems of Wiggins under some conditions. A calculating formula which determines the existence of homoclinic orbits of the systems is given.

Key words: a two-degree-of-freedom system, method of multiple scales, periodic solution, homoclinic orbit, chaos

中图分类号:

O175.14

王茂南;徐振源. ON THE HOMOCLINIC ORBITS IN A CLASS OF TWO-DEGREE-OF-FREEDOM SYSTEMS UNDER THE RESONANCE CONDITIONS[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(3): 340-352.

WANG Mao-nan;XU Zhen-yuan. ON THE HOMOCLINIC ORBITS IN A CLASS OF TWO-DEGREE-OF-FREEDOM SYSTEMS UNDER THE RESONANCE CONDITIONS[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(3): 340-352.

[1]	Shaowu YANG, Yuxin HAO, Wei ZHANG, Li YANG, Lingtao LIU. Nonlinear vibration of functionally graded graphene plateletreinforced composite truncated conical shell using first-order shear deformation theory[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(7): 981-998.
[2]	Li MA, Minghui YAO, Wei ZHANG, Dongxing CAO. Bifurcation and dynamic behavior analysis of a rotating cantilever plate in subsonic airflow[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(12): 1861-1880.
[3]	Jinchun LAN, Qianlong ZHANG, Sha WEI, Zhike PENG, Xinjian DONG, Wenming ZHANG. Uncertainty quantification for stochastic dynamical systems using time-dependent stochastic bases[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(1): 63-84.
[4]	Xiaoming LI, Shijun LIAO. Clean numerical simulation: a new strategy to obtain reliable solutions of chaotic dynamic systems[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(11): 1529-1546.
[5]	Jun HU, Shudao ZHANG. Global sensitivity analysis based on high-dimensional sparse surrogate construction[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(6): 797-814.
[6]	Yan ZHOU, Wei ZHANG. Double Hopf bifurcation of composite laminated piezoelectric plate subjected to external and internal excitations[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(5): 689-706.
[7]	A. ALGABA F.FERN′ANDEZ-S′ANCHEZ M. MERINO A.J.RODR′IGUEZ-LUIS. Comments on “Non-existence of Shilnikov chaos in continuous-time systems”[J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(9): 1175-1176.
[8]	蔡铭刘卫飞刘济科. Bifurcation and chaos of airfoil with multiple strong nonlinearities[J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(5): 627-636.
[9]	郭勇;谢建华. Neimark-Sacker (N-S) bifurcation of oscillator with dry friction in 1:4 strong resonance[J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(1): 27-36.
[10]	王波. Asymptotic analysis on weakly forced vibration of axially moving viscoelastic beam constituted by standard linear solid model[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(6): 817-828.
[11]	Z. ELHADJ J.C.SPROTT. Non-existence of Shilnikov chaos in continuous-time systems[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(3): 371-374.
[12]	刘延彬陈予恕曹庆杰. Analysis method of chaos and sub-harmonic resonance of nonlinear system without small parameters[J]. Applied Mathematics and Mechanics (English Edition), 2011, 32(1): 1-10.
[13]	柴元吕翎赵鸿雁. Lag synchronization between discrete chaotic systems with diverse structure[J]. Applied Mathematics and Mechanics (English Edition), 2010, 31(6): 733-738.
[14]	徐昌进唐先华廖茂新. Local Hopf bifurcation and global existence of periodic solutions in TCP system[J]. Applied Mathematics and Mechanics (English Edition), 2010, 31(6): 775-786.
[15]	张善元刘志芳. Nonlinear flexural waves and chaos behavior in finite-deflection Timoshenko beam[J]. Applied Mathematics and Mechanics (English Edition), 2010, 31(11): 1347-1358.

ON THE HOMOCLINIC ORBITS IN A CLASS OF TWO-DEGREE-OF-FREEDOM SYSTEMS UNDER THE RESONANCE CONDITIONS

ON THE HOMOCLINIC ORBITS IN A CLASS OF TWO-DEGREE-OF-FREEDOM SYSTEMS UNDER THE RESONANCE CONDITIONS

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价