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

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Journal of Vibration and Shock ›› 2016, Vol. 35 ›› Issue (3) : 73-78.

WANG Fang-zong LIAO Xiao-bing

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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

Key words

large-scale dynamic systems

/ fast calculation / differential quadrature method / V-transformation / multi-stage block recursive method

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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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