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Structural Engineering and Mechanics
  Volume 61, Number 1, January10 2017, pages 105-116
DOI: http://dx.doi.org/10.12989/sem.2017.61.1.105
 


Optimal extended homotopy analysis method for Multi-Degree-of-Freedom nonlinear dynamical systems and its application
Y.H. Qian and Y.F. Zhang

 
Abstract
    In this paper, the optimal extended homotopy analysis method (OEHAM) is introduced to deal with the damped Duffing resonator driven by a van der Pol oscillator, which can be described as a complex Multi-Degree-of-Freedom (MDOF) nonlinear coupling system. Ecumenically, the exact solutions of the MDOF nonlinear coupling systems are difficult to be obtained, thus the development of analytical approximation becomes an effective and meaningful approach to analyze these systems. Compared with traditional perturbation methods, HAM is more valid and available, and has been widely used for nonlinear problems in recent years. Hence, the method will be chosen to study the system in this article. In order to acquire more suitable solutions, we put forward HAM to the OEHAM. For the sake of verifying the accuracy of the above method, a series of comparisons are introduced between the results received by the OEHAM and the numerical integration method. The results in this article demonstrate that the OEHAM is an effective and robust technique for MDOF nonlinear coupling systems. Besides, the presented methods can also be broadly used for various strongly nonlinear MDOF dynamical systems.
 
Key Words
    optimal extended homotopy analysis method; Duffing resonator; van der Pol oscillator; coupling stiffness; Multi-Degree-of-Freedom
 
Address
Y.H. Qian and Y.F. Zhang: College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, Zhejiang 321004, P.R. China
 

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