The Rapid Series Method for Solving Differential Equation of the Odd Power Oscillator


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The new rapid series method to solve the differential equation of the periodic vibration of the strongly odd power nonlinear oscillator has been put forward in this paper. By adding the exponentially decaying factor to each harmonic term of the Fourier series of the periodic solution, the high accurate solution can be obtained with a few harmonic terms. The number of truncated terms is determined by the requirement of accuracy. Comparing with other approximate methods, the calculation of rapid series method is very easy and the accurate degrees of solution can be control. By comparing the analytical approximate solutions obtained by this method with numerical solutions of the cubic and fifth power oscillators, it is proven that this method is valid.



Edited by:

Chunliang Zhang and Paul P. Lin




S. L. He and Y. Huang, "The Rapid Series Method for Solving Differential Equation of the Odd Power Oscillator", Applied Mechanics and Materials, Vols. 226-228, pp. 138-141, 2012

Online since:

November 2012




[1] Y.Z. Liu and L.Q. Chen: Non-linear Vibration (Higher Education Press, China 2001) (in Chinese).

[2] T. Kapitaniak: Chaos for Engineers (Second Revised Edition, Springer, German 2000), p.1.

[3] D.X. Xi and Q. Xi: Non-linear physics (The Press of Nanjing University, China 2007), p.65.

[4] S.H. Chen: Quantitative analysis method for strongly nonlinear system (Science Press, China 2007) (in Chinese).

[5] Y. A. Rossikhin and M.V. Shitikova: Shock and Vibration, Vol. 16 (2009), p.365.

[6] J. H. He: International Journal of Modern Physics B, Vol. 20 (2006), p.1141.

[7] L.M. Wang and J.W. Liu: College Physics, Vol. 27(2008) No. 10, p.18 (in Chinese).