Abstract
In this paper, an asymptotic method is presented for the analysis of a class of strongly nonlinear autonomous oscillators. The equations governing the amplitude and phase factor are obtained, and the amplitude and stability of the corresponding limit cycles are determined.
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References
Chien Wei-zang (ed.),Singular Perturbation Theory and Its Applications in Mechanics, Science Press, Beijing (1981). (in Chinese).
Kevorkian, J. and J. D. Cole,Perturbation Methods in Applied Mathematics, Springer-Verlag, New York (1981).
Kuzmak, G. E., Asymptotic solutions of nonlinear second order diffential equations with variable cofficients,PMM (USSR),23 (1959), 515–526 (in Russian)
Luke, J. C., A perturbation method for nonlinear dispersive wave problems,Proc. Roy. Soc. Ser. A292 (1966), 403–412.
Whitham, G. B.,Linear and Nonlinear Waves, John Wiley & Sons, Inc., New York (1974).
Burton, T. D., Non-linear oscillator limit cycle analysis using a time transformation approach,Int. J. Non-Linear Mech.,17 (1982), 7–19.
Bogoliubov, N. N. and Y. A. Mitropolsky,Asymptotic Methods in the Theory of Nonlinear Oscillations, 4th Ed., “Nauka” Press, Moscow (1974). (in Russian).
Byrd, P. F. and M. D. Friedman,Handbook of Elliptic Integrals for Engineers and Scientists, 2nd Ed., Springer-Verlag, New York (1971).
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Shi-qiang, D. Asymptotic analysis of strongly nonlinear oscillators. Appl Math Mech 6, 409–415 (1985). https://doi.org/10.1007/BF01895378
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DOI: https://doi.org/10.1007/BF01895378