@article { author = {Anjum, Naveed and He, Ji-Huan}, title = {Two Modifications of the Homotopy Perturbation Method for ‎Nonlinear Oscillators}, journal = {Journal of Applied and Computational Mechanics}, volume = {6}, number = {Special Issue}, pages = {1420-1425}, year = {2020}, publisher = {Shahid Chamran University of Ahvaz}, issn = {2383-4536}, eissn = {2383-4536}, doi = {10.22055/jacm.2020.34850.2482}, 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}, url = {https://jacm.scu.ac.ir/article_16040.html}, eprint = {https://jacm.scu.ac.ir/article_16040_3f33112faf55c84e72df15f4bbf0a50d.pdf} }