THE ENHANCED HOMOTOPY PERTURBATION METHOD FOR AXIAL VIBRATION OF STRINGS

被引：130
作者：
He, Ji-Huan [1 ,2 ,3 ]
El-Dib, Yusry O. [4 ]
机构：
[1] Xian Univ Architecture & Technol, Sch Sci, Xian, Peoples R China
[2] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo, Henan, Peoples R China
[3] Soochow Univ, Coll Text & Clothing Engn, Natl Engn Lab Modern Silk, Suzhou, Peoples R China
[4] Ain Shams Univ, Fac Educ, Dept Math, Cairo, Egypt
来源：
FACTA UNIVERSITATIS-SERIES MECHANICAL ENGINEERING | 2021年 / 19卷 / 04期
关键词：
Homotopy Perturbations Method; Exponential Decay Parameter; Damping Duffing Equation; Damping Nonlinear Klein-Gordon Equation; GORDON-SCHRODINGER EQUATIONS; UNIFORM DECAY; INSTABILITY;
D O I：
10.22190/FUME210125033H
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
A governing equation is established for string axial vibrations with temporal and spatial damping forces by the Hamilton principle. It is an extension of the well-known Klein-Gordon equation. The classical homotopy perturbation method (HPM) fails to analyze this equation, and a modification with an exponential decay parameter is suggested. The analysis shows that the amplitude behaves as an exponential decay by the damping parameter. Furthermore, the frequency equation is established and the stability condition is performed. The modified homotopy perturbation method yields a more effective result for the nonlinear oscillators and helps to overcome the shortcoming of the classical approach. The comparison between the analytical solution and the numerical solution shows an excellent agreement.
引用
收藏
页码：735 / 750
页数：16
相关论文
共 35 条
  • [1] EXPONENTIAL DECAY FOR THE COUPLED KLEIN-GORDON-SCHRODINGER EQUATIONS WITH LOCALLY DISTRIBUTED DAMPING
    Almeida, A. F.
    Cavalcanti, M. M.
    Zanchetta, J. P.
    [J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2018, 17 (05) : 2039 - 2061
  • [2] Uniform decay for the coupled Klein-Gordon-Schrodinger equations with locally distributed damping
    Bisognin, V.
    Cavalcanti, M. M.
    Cavalcanti, V. N. Domingos
    Soriano, J.
    [J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2008, 15 (1-2): : 91 - 113
  • [3] Global existence and uniform decay for the coupled Klein-Gordon-Schrodinger equations
    Cavalcanti, MM
    Cavalcanti, VND
    [J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2000, 7 (03): : 285 - 307
  • [4] El-Dib YO., 2018, NONLINEAR SCI LETT A, V9, P349
  • [5] El-Dib YO., 2017, Nonlinear Sci Lett A, V8, P352
  • [6] Stability Analysis of a Damped Nonlinear Wave Equation
    El-Dib, Yusry O.
    Moatimid, Galal M.
    Elgazery, Nasser S.
    [J]. JOURNAL OF APPLIED AND COMPUTATIONAL MECHANICS, 2020, 6 : 1394 - 1403
  • [7] EFFECT OF FRACTIONAL DERIVATIVE PROPERTIES ON THE PERIODIC SOLUTION OF THE NONLINEAR OSCILLATIONS
    El-Dib, Yusry O.
    Elgazery, Nasser S.
    [J]. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2020, 28 (07)
  • [8] A Nonlinear Azimuthal Instability of Hydromgantic Rigid-Rotating Column
    El-Dib, Yusry O.
    Moatimid, Galal M.
    Mady, Amal A.
    [J]. CHINESE JOURNAL OF PHYSICS, 2020, 66 : 285 - 300
  • [9] A novelty to the nonlinear rotating Rayleigh-Taylor instability
    El-Dib, Yusry O.
    Moatimid, Galal M.
    Mady, Amal A.
    [J]. PRAMANA-JOURNAL OF PHYSICS, 2019, 93 (05):
  • [10] Stability Configuration of a Rocking Rigid Rod over a Circular Surface Using the Homotopy Perturbation Method and Laplace Transform
    El-Dib, Yusry O.
    Moatimid, Galal M.
    [J]. ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING, 2019, 44 (07) : 6581 - 6591
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