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Shock and Vibration
Volume 3 (1996), Issue 4, Pages 279-285

A Modified Lindstedt–Poincaré Method for a Strongly Nonlinear System with Quadratic and Cubic Nonlinearities

S.H. Chen1 and Y. K. Cheung2

1Department of Applied Mechanics and Engineering, Zhongshan University, Cuangzhou, China
2Department of Civil and Structural Engineering, University of Hong Kong, Hong Kong

Received 17 January 1995; Accepted 16 October 1995

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A modified Lindstedt–Poincaré method is presented for extending the range of the validity of perturbation expansion to strongly nonlinear oscillations of a system with quadratic and cubic nonlinearities. Different parameter transformations are introduced to deal with equations with different nonlinear characteristics. All examples show that the efficiency and accuracy of the present method are very good.