Recently I suggested a simple method for nonlinear oscillators , you can download the paper by the following link
http://works.bepress.com/ji_huan_he/105/
is this frequency formulation the simplest one? can we development the method to be an iteration algorithm?
This paper suggests the simplest approach (labelled as He's frequency formulation in open literature ) to nonlinear oscillators with relatively high accuracy. The obtained result can be used as a good initial solution for the variational iteration method and the homotopy perturbation method if a higher accuracy is still needed. This short paper sheds a bright light on fast insight into the periodic property of a nonlinear oscillator. Please refer to the following reviewer article for detailed derivation of the formulation: He JH. The simpler, the better: Analytical methods for nonlinear oscillators and fractional oscillators, Journal of Low Frequency Noise, Vibration and Active Control , 2019 DOI: 10.1177/1461348419844145 journals.sagepub.com/home/lfn
With Best Regards
Sincerely Yours
Ji-Huan He
Please look at the following below links which may help you in your analysis:
https://www.researchgate.net/publication/222050383_Solution_of_a_quadratic_nonlinear_oscillator_by_the_method_of_harmonic_balance
https://reader.elsevier.com/reader/sd/pii/S1110016816300199?token=D65A9E8122BD56D95B47BC2374AF3731CD6FC9C5413C696E12FCBDAF45D27971B56640C88AA6FEDA9B4A8A97FAC415E2
https://hal.archives-ouvertes.fr/hal-01696203/document
Thanks
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