Approximately Analytic Solution of the Differential Equation of Damped Odd Power Oscillator

Abstract:

The approximately analytic solution of the differential equation of the damped vibration of the strongly odd power nonlinear oscillator has been obtained by harmonically averaging method. By comparing with numerical results, it is proven that the principle of the attenuation of amplitude gotten by this method is almost exact, and the approximate solution is valid.

• Periodical: Applied Mechanics and Materials (Volumes 488-489)
• Pages: 1185-1188
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.488-489.1185
• Online since: January 2014
• Authors: Yuan Huang*
• Keywords: Approximately Analytic Solution, Damped Vibration, Odd Power Oscillator

References

[1] Liu Yan-Zhu, Chen Li-qun, Non-linear Vibration, Higher Education Press, Beijing(2001)(in Chinese).

[2] Chen Shu-hui, Quantitative analysis method for strongly nonlinear system, Science Press, Beijing (2007) (in Chinese).

[3] J.H. He, Communications in NonlinearScience and NumericalSimulation 3 (1998) 92–97.

[4] L. Cveticanin, Chaos, Solitons and Fractals 30 (2006)1221–1230.

[5] L. Cveticanin, International Journal of Nonlinear Sciences and Numerical Simulation 10 (2009)1491–1516.

[6] J. H. He, Int. J. Mod. Phys. B 20(2006), 1141.

[7] Yuste S B, Bejarano J D, J. Sound and Vibration 110(2)(1986)347.

[8] Liu Hui-yin, Essentials of MATLAB R2007, Tsinghua University Press, Beijing (2008) (in Chinese).