任意激励下无阻尼系统求解的整体自适应方法

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振动与冲击 ›› 2020, Vol. 39 ›› Issue (23) : 47-51.

论文

陈东良，王联甫，臧睿，周长鹤，宫臣，张金东

作者信息 +

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

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

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文章历史 +

摘要

针对无阻尼系统求解的计算精度和效率问题，进行了整体自适应精细积分法的研究。采用Padé逼近和Simpson公式，分析解方程中矩阵指数和Duhamel积分项的精细参数之间的关系，据此，提出了振动微分方程组求解的整体自适应精细积分法。该方法可以根据不同的精度要求进行自适应积分，对高频激励依旧能保证其计算精度。这对于求解高频激励下的振动响应和提高计算效率都是有益的。数值算例验证了该方法的有效性。

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.

导出引用

陈东良，王联甫，臧睿，周长鹤，宫臣，张金东. 任意激励下无阻尼系统求解的整体自适应方法[J]. 振动与冲击, 2020, 39(23): 47-51

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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