Journal of Applied and Computational Mechanics
Two Modifications of the Homotopy Perturbation Method for Nonlinear Oscillators
Document Type : Research Paper
Authors
1 National Engineering Laboratory for Modern Silk, College of Textile and Engineering, Soochow University, Suzhou, China
2 School of Mathematical Sciences, Soochow University, Suzhou, China
3 Department of Mathematics, Government College University, Faisalabad, Pakistan
4 School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, China
5 School of Science, Xi'an University of Architecture and Technology, Xi’an, China
Abstract
Nonlinear vibration arises in engineering and physics, and the periodic motion of these nonlinear oscillatory systems have rich dynamics. An estimation of amplitude-frequency relationship of a nonlinear oscillator is much needed, therefore, well-known homotopy perturbation method is employed for this purpose. In this paper, two last modifications of the homotopy perturbation method are briefly reviewed, which couples with either the parameter-expansion technology or the enhanced perturbation method. Both modifications are extremely effective for nonlinear oscillators, and the cubic-quintic-septic Duffing oscillator is used as an example to elucidate the solution processes.
Keywords
- Homotopy perturbation method
- Enhanced perturbation method
- Amplitude-frequency relationship
- Duffing oscillators
- Periodic solution
Main Subjects
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