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Homotopy Analysis Method for Large-Amplitude Free Vibrations of Strongly Nonlinear Generalized Duffing Oscillators
College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, China
College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, China
College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, China
College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, China
- 1 College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, China
- 2 College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, China
- 3 College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, China
- 4 College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, China
Modern Mechanical Engineering·Volume 02 (2012)·Pages 167–175·Published 28 November 2012·DOI10.4236/mme.2012.24022
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Abstract
In this study, the homotopy analysis method (HAM) is used to solve the generalized Duffing equation. Both the frequencies and periodic solutions of the nonlinear Duffing equation can be explicitly and analytically formulated. Accuracy and validity of the proposed techniques are then verified by comparing the numerical results obtained based on the HAM and numerical integration method. Numerical simulations are extended for even very strong nonlinearities and very good correlations which achieved between the results. Besides, the optimal HAM approach is introduced to accelerate the convergence of solutions.
KeywordsStrongly Nonlinear VibrationGeneralized Duffing EquationHomotopy Analysis Method
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