Bifurcations and Exact Solutions of a Cantilever Beam Vibration Model Without Damping and Forced Terms

被引：1
|
作者：
Zhuang, Jinsen [1 ]
Chen, Guanrong [2 ]
Li, Jibin [1 ,3 ]
机构：
[1] Huaqiao Univ, Sch Math Sci, Quanzhou 362021, Fujian, Peoples R China
[2] City Univ Hong Kong, Dept Elect Engn, Hong Kong, Peoples R China
[3] Zhejiang Normal Univ, Sch Math Sci, Jinhua 321004, Zhejiang, Peoples R China
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2024年 / 34卷 / 03期
关键词：
Nonlinear vibration; cantilever beam model; singular nonlinear equation; bifurcation; homoclinic and heteroclinic solutions; periodic solution; peakon; periodic peakon; compacton; SOLITONS; EQUATION;
D O I：
10.1142/S0218127424500391
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For the cantilever beam vibration model without damping and forced terms, the corresponding differential system is a planar dynamical system with some singular straight lines. In this paper, by using the techniques from dynamical systems and singular traveling wave theory developed by [Li & Chen, 2007] to analyze its corresponding differential system, the bifurcations and the dynamical behaviors of the corresponding phase portraits are identified and analyzed. Under different parameter conditions, exact homoclinic and heteroclinic solutions, periodic solutions, compacton solutions, as well as peakons and periodic peakons, are all found explicitly.
引用
收藏
页数：21
相关论文
共 50 条
  • [21] ON THE SOLUTIONS FOR AN EXTENSIBLE BEAM EQUATION WITH INTERNAL DAMPING AND SOURCE TERMS
    Pereira, Ducival C.
    Nguyen, Hoang
    Raposo, Carlos A.
    Maranhao, Celsa H. M.
    DIFFERENTIAL EQUATIONS & APPLICATIONS, 2019, 11 (03): : 367 - 377
  • [22] Unboundedness of Solutions of Timoshenko Beam Equations with Damping and Forcing Terms
    Kobayashi, Kusuo
    Yoshida, Norio
    INTERNATIONAL JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 2013
  • [23] VIBRATION CONTROL OF A CANTILEVER BEAM USING REDUCED MODEL
    Kamalirad, Amir Mohamad
    Fotouhi, Reza
    Taghizadeh, Mitra
    PROCEEDINGS OF ASME 2022 INTERNATIONAL MECHANICAL ENGINEERING CONGRESS AND EXPOSITION, IMECE2022, VOL 5, 2022,
  • [24] BIFURCATIONS AND EXACT TRAVELING WAVE SOLUTIONS OF GERDJIKOV-IVANOV EQUATION WITH PERTURBATION TERMS
    Zhu, Wenjing
    Xia, Yonghui
    Bai, Yuzhen
    ADVANCES IN DIFFERENTIAL EQUATIONS, 2020, 25 (5-6) : 279 - 314
  • [25] Bifurcations and Exact Solutions in a Model of Hydrogen-Bonded-Chains
    Li, Jibin
    Chen, Fengjuan
    Tchakoutio-Nguetcho, A. S.
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2015, 25 (04):
  • [26] Nonlinear forced vibration analysis of a rotating three-dimensional tapered cantilever beam
    Zhou, Yanxun
    Zhang, Yimin
    Yao, Guo
    JOURNAL OF VIBRATION AND CONTROL, 2021, 27 (15-16) : 1879 - 1892
  • [27] Analysis on jump and bifurcation phenomena in the forced vibration of nonlinear cantilever beam using HBM
    Motallebi, A.
    Irani, S.
    Sazesh, S.
    JOURNAL OF THE BRAZILIAN SOCIETY OF MECHANICAL SCIENCES AND ENGINEERING, 2016, 38 (02) : 515 - 524
  • [28] Effects of Variations in Nonlinear Damping Coefficients on the Parametric Vibration of a Cantilever Beam with a Lumped Mass
    Silva, Demian G.
    Varoto, Paulo S.
    MATHEMATICAL PROBLEMS IN ENGINEERING, 2008, 2008
  • [29] Analysis on jump and bifurcation phenomena in the forced vibration of nonlinear cantilever beam using HBM
    A. Motallebi
    S. Irani
    S. Sazesh
    Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2016, 38 : 515 - 524
  • [30] Vibration damping analysis of the laminated composite sandwich cantilever beam inserted with viscoelastic layer
    Yim, JH
    Cho, SY
    Seo, YJ
    PROCEEDINGS OF ISMA 2002: INTERNATIONAL CONFERENCE ON NOISE AND VIBRATION ENGINEERING, VOLS 1-5, 2002, : 2299 - 2305
12345