Overall self-adaptive precision integration method for solving an undamped system under arbitrary excitation

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Journal of Vibration and Shock ›› 2020, Vol. 39 ›› Issue (23) : 47-51.

CHEN Dongliang, WANG Lianfu, ZANG Rui, ZHOU Changhe, GONG Chen, ZHANG Jindong

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Abstract

Aiming at calculation precision and efficiency problems of solving an undamped system, the overall self-adaptive precision integration method was studied.Padé approximation and Simpson formula were used to analyze the relationship between matrix exponent and fine parameters of Duhamel integral term in solving differential equations, and then the overall self-adaptive precision integration method for solving a vibration differential equation set was proposed.It was shown that thismethod can be used to do self-adaptive integration according to different precision requirements, and keep its computational accuracy under high frequency excitation; this method is beneficial to solve vibration responses under high frequency excitation and improve computational efficiency.Numerical examples verified the effectiveness of the proposed method.

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Padé / approximation / Duhamel integral / self-adaptive / precision integration

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CHEN Dongliang, WANG Lianfu, ZANG Rui, ZHOU Changhe, GONG Chen, ZHANG Jindong. Overall self-adaptive precision integration method for solving an undamped system under arbitrary excitation[J]. Journal of Vibration and Shock, 2020, 39(23): 47-51

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