Analytical solutions to nonlinear conservative oscillator with fifth-order nonlinearity

被引：0
作者：
M. G. Sfahani
S. S. Ganji
Amin Barari
H. Mirgolbabaei
G. Domairry
机构：
[1] Babol University of Technology,Departments of Civil and Mechanical Engineering
[2] Islamic Azad University,Department of Transportation Engineering
[3] Science and Research Branch,Department of Civil Engineering
[4] Aalborg University,undefined
[5] Department of Mechanical Engineering Islamic Azad University,undefined
[6] Ghaemshahr branch,undefined
来源：
Earthquake Engineering and Engineering Vibration | 2010年 / 9卷
关键词：
non-linear oscillation; homotopy perturbation method (HPM); max-min approach (MMA); Rung-Kutta method (R-KM); large amplitude free vibrations;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper describes analytical and numerical methods to analyze the steady state periodic response of an oscillator with symmetric elastic and inertia nonlinearity. A new implementation of the homotopy perturbation method (HPM) and an ancient Chinese method called the max-min approach are presented to obtain an approximate solution. The major concern is to assess the accuracy of these approximate methods in predicting the system response within a certain range of system parameters by examining their ability to establish an actual (numerical) solution. Therefore, the analytical results are compared with the numerical results to illustrate the effectiveness and convenience of the proposed methods.
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页码：367 / 374
页数：7
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  • [1] Barari A.(2008)Variational Iteration Method and Homotopy-Perturbation Method for Solving Different Types of Wave Equations Journal of Applied Sciences 8 120-126
  • [2] Ghotbi Abdoul R.(2008)Application of Homotopy Perturbation Method and Variational Iteration Method to Nonlinear Oscillator Differential Equations Acta Applicanda Mathematicae 104 161-171
  • [3] Farrokhzad F.(2007)Application of a Modified He’s Homotopy Perturbation Method to Obtain Higher-Order Approximations of an Physics Letters A 371 421-166
  • [4] Ganji D.D.(2008) Force Nonlinear Oscillator Applied Mathematical Modeling 32 1744-8
  • [5] Barari A.(2004)Solution of Free Vibration Equations of Beam on Elastic Soil by Using Differential Transform Method International Journal of Computer Mathematics 81 25-2159
  • [6] Omidvar M.(2008)The Use of Adomian Decomposition Method for Solving the One-Dimensional Parabolic Equation with Non-local Boundary Specifications Physica Scripta 78 1-173
  • [7] Ghotbi Abdoul R.(2009)The Use of the Decomposition Procedure of Adomian for Solving a Delay Differential Equation Arising in Electrodynamics Mathematical Methods in the Applied Sciences 33 157-135
  • [8] Ganji D.D.(2009)Application of Amplitude-frequency Formulation to Nonlinear Oscillation System of the Motion of a Rigid Rod Rocking Back International Journal of Modern Physics B 23 461-393
  • [9] Beléndez A.(2009)He’s Energy Balance and He’s Variational Methods for Nonlinear Oscillations in Engineering International Journal of Non-Linear Sciences and Numerical Simulation 10 303-undefined
  • [10] Pascual C.(2009)Applications of He’s Homotopy Perturbation Method to Obtain Second-order Approximations of the Coupled Two-degree-of-freedom Systems International Journal of Modern Physics B 23 435-undefined
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