@inproceedings{1e0139b0f6c34035a5f5133004e40853,
title = "The method of multiple scales in solving nonlinear dynamic differential equations of gear systems",
abstract = "To obtain exact analytical solutions of differential equations of gear system dynamics due to the difficulty of solving complicated differential equations. Only the approximate analytical solutions can be determined. The method of multiple scales is one of the most powerful, popular perturbation methods. The dynamic model which describes the torsional vibration behaviors of gear system has been introduced accurately in this paper. The differential equation of gear system nonlinear dynamics exhibiting combined nonlinearity influence such as time-varying stiffness, tooth backlash and dynamic transmission error (DTE) has been proposed. The theory of multiple scales method has been presented in solving nonlinear differential equations of gear systems and the frequency response equation has been obtained. The fact that the approximate analytical solution by using the method of multiple scales is in good agreement with the exact solutions by numerically integrating differential equations has proved that the method of multiple scales is one of the most frequently used methods in solving differential equations, especially for large and complicated differential equations.",
keywords = "Analytical solutions;, Gear systems, Multiple scales, Nonlinear oscillations",
author = "Nie, \{J. F.\} and Zheng, \{M. L.\} and Yu, \{G. B.\} and Wen, \{J. M.\} and B. Dai",
year = "2013",
doi = "10.4028/www.scientific.net/AMM.274.324",
language = "英语",
isbn = "9783037855904",
series = "Applied Mechanics and Materials",
publisher = "Trans Tech Publications Ltd",
pages = "324--327",
booktitle = "Mechanical Engineering, Materials Science and Civil Engineering",
address = "瑞士",
note = "2012 International Conference on Mechanical Engineering, Materials Science and Civil Engineering, ICMEMSCE 2012 ; Conference date: 18-08-2012 Through 20-08-2012",
}