An improved KBM method for solving nonlinear vibration equations

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Journal of Vibration and Shock ›› 2018, Vol. 37 ›› Issue (13) : 165-170.

WANG Leijia，ZHANG Huzhi，HU Hui，ZHU Mingqiao

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Abstract

The classical KBM method can be used to solve nonlinear vibration equations with small parameters, but these small parameters greatly restrict the application of the classical KBM method. Here, the square modification was done for the basic equation of frequency expression in the classical KBM method so that the solving range of the method could not be restrained by small parameters. The improved KBM method was used to solve Duffing equation. In calculation, the frequency equation of the vibration system was simplified. The equation’s quadratic approximate solution and frequency solution were compared with solutions of other methods. It was shown that the feasibility of the improved KBM method is verified; the accuracy of its calculation results is higher than that of other methods.

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non-linear vibration / Krylov-Bogoliubov-Mitropolsky method / improve KBM method / Duffing equation

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WANG Leijia，ZHANG Huzhi，HU Hui，ZHU Mingqiao. An improved KBM method for solving nonlinear vibration equations[J]. Journal of Vibration and Shock, 2018, 37(13): 165-170

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