This paper aims to improve the accuracy of time integration algorithms (TIAs) for long-term simulation of structural dynamics. To this end, a new method of reducing the period elongation (numerical dispersion) was proposed by utilizing the mass scaling matrix. Firstly, the period elongation of explicit Gui-[Formula: see text] algorithm as a representative was analyzed, and the strategy of enhancing the algorithm accuracy was investigated. Subsequently, the period elongation was reduced by introducing a parameter to change the mass matrix, which is weighted by the original mass matrix and stiffness matrix. The bisection method is utilized to determine the parameter according to the formulation of period elongation. Since just the mass matrix of original algorithm is changed slightly, the convergence rate of original TIA remains unchanged and the proposed mass scaling method imposes little influence on the stability condition of original algorithm. Moreover, this method has few modifications to the computer program of TIA and is easy to implement. Finally, both linear and nonlinear long-term dynamic response analyses for multiple-degree-of-freedom systems indicated that the proposed mass scaling method is effective and convenient to reduce the period elongation for several typical TIAs.

中文翻译：

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一种提高长期运动仿真时间积分算法精度的方法

本文旨在提高用于结构动力学长期仿真的时间积分算法 (TIA) 的准确性。为此，提出了一种利用质量缩放矩阵来降低周期伸长率（数值色散）的新方法。首先，分析了以显式Gui-[公式：见正文]算法为代表的周期延长，研究了提高算法精度的策略。随后，通过引入一个参数来改变质量矩阵，从而降低周期伸长率，该质量矩阵由原始质量矩阵和刚度矩阵加权。采用二分法根据周期延长的公式确定参数。由于只是对原算法的质量矩阵稍作改动，原始TIA的收敛速度保持不变，提出的质量缩放方法对原始算法的稳定性条件影响很小。此外，该方法对TIA的计算机程序修改少，易于实现。最后，多自由度系统的线性和非线性长期动态响应分析表明，所提出的质量缩放方法可以有效且方便地减少几种典型 TIA 的周期伸长。