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Article

A Generalized KBM Method for Strongly Nonlinear Oscillators with Slowly Varying Parameters

by
Jianping Cai
1,2
1
Department of Applied Mechanics and Engineering, Zhongshan University, Guangzhou 510275, China
2
Department of Mathematics, Zhangzhou Teachers College, Fujian 363000, China
Math. Comput. Appl. 2007, 12(1), 21-30; https://doi.org/10.3390/mca12010021
Published: 1 April 2007
Versions Notes

Abstract

A generalized Krylov-Bogoliubov-Mitropolsky (KBM) method is extended for the study of strongly nonlinear oscillators with slowly varying parameters. The asymptotic amplitude and phase are derived and then the asymptotic solutions of arbitrary order are obtained theoretically. Cubic nonlinear oscillators with polynomial damping are studied in detail. Three examples are considered: a generalized Van der Pol oscillator, a Rayleigh equation and a pendulum with variable length. Comparisons are also made with numerical solutions to show the efficiency and accuracy of the present method.
Keywords: strongly nonlinear oscillation; KBM method; slowly varying parameter strongly nonlinear oscillation; KBM method; slowly varying parameter

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MDPI and ACS Style

Cai, J. A Generalized KBM Method for Strongly Nonlinear Oscillators with Slowly Varying Parameters. Math. Comput. Appl. 2007, 12, 21-30. https://doi.org/10.3390/mca12010021

AMA Style

Cai J. A Generalized KBM Method for Strongly Nonlinear Oscillators with Slowly Varying Parameters. Mathematical and Computational Applications. 2007; 12(1):21-30. https://doi.org/10.3390/mca12010021

Chicago/Turabian Style

Cai, Jianping. 2007. "A Generalized KBM Method for Strongly Nonlinear Oscillators with Slowly Varying Parameters" Mathematical and Computational Applications 12, no. 1: 21-30. https://doi.org/10.3390/mca12010021

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