Solution of Cubic-Quintic Duffing Oscillators using Harmonic Balance Method

被引：0
|
作者：
Hosen, M. A. [1 ,2 ]
Chowdhury, M. S. H. [2 ]
机构：
[1] Rajshahi Univ Engn & Technol, Dept Math, Rajshahi 6204, Bangladesh
[2] Int Islam Univ Malaysia, Kulliyyah Engn, Dept Engn Sci, Kuala Lumpur 50728, Malaysia
来源：
MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES | 2016年 / 10卷
关键词：
Approximate frequency; Harmonic balance method; Cubicquintic Duffing oscillator; Analytical solutions;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this study, Harmonic Balance Method (HBM) is applied to determine approximate analytic solutions of strongly nonlinear Duffing oscillators with cubic-quintic nonlinear restoring force. Mainly, a set of nonlinear algebraic equations is solved in this method. The new method avoids the necessity of numerically solving sets of algebraic equations with very complex nonlinearities. Numerical comparisons between the HBM and the exact solutions reveal that the HBM is a promising tool for strongly nonlinear oscillator's problems.
引用
收藏
页码：181 / 192
页数：12
相关论文
共 50 条
  • [21] An Innovative Approach in Inspecting a Damped Mathieu Cubic-Quintic Duffing Oscillator
    Moatimid, Galal M.
    Mohamed, Mona A. A.
    Elagamy, Khaled
    JOURNAL OF VIBRATION ENGINEERING & TECHNOLOGIES, 2024, 12 : 1831 - 1848
  • [22] An integral of motion for the damped cubic-quintic Duffing oscillator with variable coefficients
    Urenda-Cazares, E.
    Gallegos, A.
    Macias-Diaz, J. E.
    Vargas-Rodriguez, H.
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2019, 78
  • [23] On the modeling of a parametric cubic-quintic nonconservative Duffing oscillator via the modified homotopy perturbation method
    El-Dib, Yusry O.
    Elgazery, Nasser S.
    Mady, Amal A.
    Alyousef, Haifa A.
    ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, 2022, 77 (05): : 475 - 486
  • [24] Solution of a Duffing-harmonic oscillator by the method of harmonic balance
    Hu, H.
    Tang, J. H.
    JOURNAL OF SOUND AND VIBRATION, 2006, 294 (03) : 637 - 639
  • [25] AN EFFICIENT APPROACH FOR SOLVING THE FRACTAL, DAMPED CUBIC-QUINTIC DUFFING'S EQUATION
    Elias-Zuniga, Alex
    Martinez-romero, Oscar
    Trejo, Daniel olvera
    Palacios-pineda, Luis manuel
    FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2024, 32 (01)
  • [26] Dynamics of cubic-quintic nonlinear PT-symmetry mechanical oscillators
    Azeghap-Simo, Ibrahim
    Fotsa-Ngaffo, Fernande
    Kenfack-Jiotsa, Aurelien
    PHYSICA D-NONLINEAR PHENOMENA, 2023, 449
  • [27] Analytical Approximate Solutions for the Cubic-Quintic Duffing Oscillator in Terms of Elementary Functions
    Belendez, A.
    Alvarez, M. L.
    Frances, J.
    Bleda, S.
    Belendez, T.
    Najera, A.
    Arribas, E.
    JOURNAL OF APPLIED MATHEMATICS, 2012,
  • [28] Exact solution for the unforced Duffing oscillator with cubic and quintic nonlinearities
    Belendez, A.
    Belendez, T.
    Martinez, F. J.
    Pascual, C.
    Alvarez, M. L.
    Arribas, E.
    NONLINEAR DYNAMICS, 2016, 86 (03) : 1687 - 1700
  • [29] The iterative homotopy harmonic balance method for conservative Helmholtz-Duffing oscillators
    Guo, Zhongjin
    Leung, A. Y. T.
    APPLIED MATHEMATICS AND COMPUTATION, 2010, 215 (09) : 3163 - 3169
  • [30] Exact solution for the unforced Duffing oscillator with cubic and quintic nonlinearities
    A. Beléndez
    T. Beléndez
    F. J. Martínez
    C. Pascual
    M. L. Alvarez
    E. Arribas
    Nonlinear Dynamics, 2016, 86 : 1687 - 1700
12345