基于微分求积法及V-变换的大规模动力系统快速数值计算方法

汪芳宗, 廖小兵

振动与冲击 ›› 2016, Vol. 35 ›› Issue (3) : 73-78.

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振动与冲击 ›› 2016, Vol. 35 ›› Issue (3) : 73-78.
论文

基于微分求积法及V-变换的大规模动力系统快速数值计算方法

  • 汪芳宗, 廖小兵
作者信息 +

Fast numerical calculation method for large-scale dynamic systems based on differential quadrature method and V-transformation#br#

  •  WANG Fang-zong   LIAO Xiao-bing
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文章历史 +

摘要

针对大规模动力系统动态响应的数值计算,传统的微分求积法通常在时间域上逐步离散、整体求解,存在“维数灾”问题。在多级高阶时域微分求积法的基础上,提出了基于V-变换的大规模动力系统动态响应的快速数值计算方法。利用微分求积法的加权系数矩阵满足V-变换这一重要特性,将离散后的雅可比矩阵方程进行解耦分块,推导形成了多级分块递推计算方法。数值算例表明,即使采用相当于Newmark方法2s倍的步长,微分求积法的计算精度仍比Newmark方法要高出2~3个数量级。进一步对3个不同规模的算例系统进行了测试,结果表明:相对于传统的数值计算方法,多级分块递推计算方法可以获得较大的加速比,能够显著提高大规模动力系统动态响应的计算效率。

Abstract

 For numerical simulation of large-scale dynamic systems’ response, the traditional differential quadrature method (DQM) usually adopts successive discrete and global solution in time domain, where there is the problem of “curse of dimensionality”. On the basis of the multi-stage high-order time domain differential quadrature method, a fast numerical calculation method for large-scale dynamic systems’ response based on V-transformation is proposed. Using the V-transformation possessed by the weighting coefficient matrix of DQM, the whole Jacobian matrix equations involved in the traditional approach of DQM can be decoupled into blocks, thus the multi-stage block recursive method is formed. Numerical examples show that, even using 2s times step size of the Newmark method, the calculation precision of the differential quadrature method is about 2~3 orders of magnitude higher than that of the Newmark method. Furthermore, three different scale systems are used for computational efficiency test and the results show that the multi-stage block recursive method can obtain high speedups compared with the traditional numerical methods, which can significantly improve the computational efficiency of large-scale dynamic systems’ response.
Key words: large-scale dynamic systems; fast calculation; differential quadrature method; V-transformation; multi-stage block recursive method

关键词

大规模动力系统 / 快速计算 / 微分求积法 / V-变换 / 多级分块递推方法

Key words

 large-scale dynamic systems
/ fast calculation / differential quadrature method / V-transformation / multi-stage block recursive method

引用本文

导出引用
汪芳宗, 廖小兵. 基于微分求积法及V-变换的大规模动力系统快速数值计算方法[J]. 振动与冲击, 2016, 35(3): 73-78
WANG Fang-zong LIAO Xiao-bing. Fast numerical calculation method for large-scale dynamic systems based on differential quadrature method and V-transformation#br#[J]. Journal of Vibration and Shock, 2016, 35(3): 73-78

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