A New Method to Solving the Multiple Solutions of Nonlinear Vibration Equations

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Journal of Vibration and Shock ›› 2011, Vol. 30 ›› Issue (10) : 14-18.

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A New Method to Solving the Multiple Solutions of Nonlinear Vibration Equations

Qian Zheng-wen; Cheng Li; Chen Wei; Li Ying-hong

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Abstract

The initial iterative value is difficult to choose when there are multiple periodic solutions in solving the nonlinear vibration equations. Moreover, the simple iterative solution process of conventional approaches is inefficient to track the periodic solution with different outer excitation. In the view of these two problems, the homotopy method is employed so that the initial iterative value can be chosed easily. The solution curve variated with outer excitation is tracked by the predict-correct method. Both the stable and unstable periodic solutions can be calculated by using this method. The feasibility of the method is verified by calculating the Duffing oscillator equation. It is show that the simulation results using this method agrees well with the theoretic approximate results and the results using the Rung-Kuta method.

Key words

nonlinear / vibration / multiple solution / harmonic balance method / predict-correct method / homotopy method

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Qian Zheng-wen;Cheng Li;Chen Wei;Li Ying-hong. A New Method to Solving the Multiple Solutions of Nonlinear Vibration Equations[J]. Journal of Vibration and Shock, 2011, 30(10): 14-18