Abstract
In this paper, a nonlinear time transformation method is presented for the analysis of strong nonlinear oscillation systems. This method can be used to study the limit cycle behavior of the autonomous systems and to analyze the forced vibration of a strong nonlinear system.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ottoy JP. An extension of the Van der P ol oscillator. Int J Control, 1980, 31(4): 691–703
Yuste SB, Bejarano JD. Construction of approximate analytical solutions to a new class of non-linear oscillator equations. J Sound Vib, 1986, 110(2): 347–350
Burton TD. Non-linear oscillator limit cycle analysis using a time transformation approach. Int J Non-linear Mech, 1982, 17(1): 7–19
Xu Zhao. A new asymptotic method in nonlinear mechanics. Acta Mechanica Sinica, 1985, 17(3): 266–271 (in Chinese)
Xu Zhao, Zhang Lingqi, Asymptotic method for analysis of non-linear systems with two parameters. Acta Mathematica Scientia, 1986, 6(4): 453–462
Mickens RE, Perturbation procedure for the Van der Pol oscillator based on the Hopf bifurcation theorem. J Sound Vib, 1988, 127(1): 187–191
Nayfeh AH. Perturbation methods. 1nd ed. New York: Wiley, 1973
Nayfeh AH, Mook DT, Non-linear Oscillations. 1nd ed. New York: Wiley, 1979
Author information
Authors and Affiliations
Additional information
The project partly supported by the Foundation of Zhongshan University Advanced Research Center
Rights and permissions
About this article
Cite this article
Zhao, X. Nonlinear time transformation method for strong nonlinear oscillation systems. Acta Mech Sinica 8, 279–288 (1992). https://doi.org/10.1007/BF02489252
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02489252