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RESEARCH PAPERS

A Modified Lindstedt–Poincaré Method for Strongly Mixed-Parity Nonlinear Oscillators

[+] Author and Article Information
W. P. Sun

Department of Mechanics and Engineering Science, School of Mathematics, Jilin University, Changchun 130012, P.R.C.

B. S. Wu1

Department of Mechanics and Engineering Science, School of Mathematics, Jilin University, Changchun 130012, P.R.C.bswu@public.cc.jl.cn

C. W. Lim

Department of Building and Construction, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, P.R.C.

1

Corresponding author.

J. Comput. Nonlinear Dynam 2(2), 141-145 (Oct 04, 2006) (5 pages) doi:10.1115/1.2447304 History: Received July 17, 2006; Revised October 04, 2006

By introducing linear and constant terms with an undetermined parameter and subsequently using certain rules to determine the optimal value of the parameter, we establish analytical approximate frequencies and the corresponding periodic solutions for strongly mixed-parity nonlinear oscillators. A quadratic–cubic nonlinear oscillator is used to verify and illustrate the usefulness and effectiveness of the proposed method.

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Copyright © 2007 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Comparison of approximate periodic solutions with exact periodic solution: (a) A=0.1; (b) A=0.5; and (c) A=10

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