This article focuses mainly on the development of explicit integration algorithms for structural dynamics. Some known single‐step explicit schemes are first reviewed and their algorithmic parameters are uniformly given as a function of ${\rho }_b$, denoting spectral radius at the bifurcation point. The simple review reveals that there are still some problems to be addressed. Then, a simple but general explicit integration algorithm (GSSE) is presented and analyzed. Besides, a truly self‐starting explicit algorithm and the true explicit form of generalized‐ $\alpha$ method are also given. The novel GSSE algorithm possesses very significant advantages in terms of accuracy and dissipation control. The GSSE method achieves not only controllable dissipation at the bifurcation point but also the identical second‐order accuracy of three primary variables. Numerical spectral analysis and examples are provided to clearly show the superiority of novel explicit methods over other single‐step explicit ones. Hence, the novel GSSE method is highly recommended to solving general dynamical problems.

中文翻译：

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具有耗散控制的结构动力学相同的二阶单步显式积分算法

本文主要关注结构动力学的显式集成算法的开发。首先回顾一些已知的单步显式方案，并根据以下公式统一给出其算法参数：${\rho }_b$，表示分叉点处的光谱半径。简单的审查显示，仍有一些问题需要解决。然后，提出并分析了一种简单但通用的显式集成算法（GSSE）。此外，还有一个真正自启动的显式算法和广义化的真正显式形式。$\alpha$还给出了方法。新型GSSE算法在准确性和耗散控制方面具有非常重要的优势。GSSE方法不仅在分叉点实现了可控的耗散，而且实现了三个主要变量的相同的二阶精度。提供了数值频谱分析和示例，以清楚地表明新颖的显式方法优于其他单步显式方法。因此，强烈建议使用新颖的GSSE方法来解决一般动力学问题。