A modified two-variable expansion method for a nonlinear Jerk equation

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Journal Article
Zhendong yu Chongji/Journal of Vibration and Shock, 2012, 31 (23), pp. 118 - 122
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A modified two-variable expansion method was used to determine approximate frequencies and approximate analytical periodic solutions to a third-order differential equation with cubic nonlinearterms. This method combining Lindstedt-Poincare technique and the two-variable expansion method was not only valid for weakly nonlinear oscillations but also for strongly nonlinear oscillations. Here, a nonlinear Jerk equation excluding linear part of velocity term as an example was calculated. Its second-order approximate period and second-order approximate analytical periodic solution were obtained. A comparison of the first and second approximate analytical periodic solutions with the numerically exact solutions showed that the second order approximate analytical periodic solution is much more accurate than the first one. The result showed that the modified two-variable expansion method is suitable for solving a nonlinear Jerk equation, moreover, when the Jerk equation doesn't have linear part of velocity term, this method is still effective.
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