A new family of time integration methods is formulated. The recommended technique is useful and robust for the loads with large variations and the systems with nonlinear damping behavior. It is also applicable for the structures with lots of degrees of freedom, and can handle general nonlinear dynamic systems. By comparing the presented scheme with the fourth-order Runge–Kutta and the Newmark algorithms, it is concluded that the new strategy is more stable. The authors’ formulations have good results on amplitude decay and dispersion error analyses. Moreover, the family orders of accuracy are m+2 and m+3 for even and odd values of m, respectively. Findings demonstrate the superiority of the new family compared to explicit and implicit methods and dissipative and non-dissipative algorithms.

中文翻译：

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一个高效的加权剩余时间积分族

制定了一系列新的时间积分方法。推荐的技术对于具有大变化的负载和具有非线性阻尼行为的系统是有用且稳健的。它也适用于具有大量自由度的结构，可以处理一般的非线性动力系统。通过将提出的方案与四阶Runge-Kutta和Newmark算法进行比较，可以得出结论，新策略更稳定。作者的公式在幅度衰减和色散误差分析方面有很好的效果。此外，准确性的家庭顺序是米+2和米+3对于偶数和奇数的值米， 分别。研究结果表明，与显式和隐式方法以及耗散和非耗散算法相比，新系列的优越性。